With abortion and executive privilege to be two huge issues facing Samuel Alito during his confirmation hearing this week, the Supreme Court nominee said Monday that a good judge always keeps an open mind and that no person is above the law.

"A judge can't have any agenda, a judge can't have any preferred outcome in any particular case, and a judge certainly doesn't have a client ... the judge's sole obligation is to the rule of law," Alito said.

The almost 11 minutes of remarks were made without notes as the nominee tried to present his case for why he should be confirmed to replace retiring Justice Sandra Day O'Connor.

Watch gavel-to-gavel, streaming live video of day two of the Senate Judiciary Committee hearing on FOXNews.com, beginning at 9:30 a.m. EST Tuesday.

He added that good judges develop good habits, such as delaying reaching conclusions until everything has been considered.

"Good judges are always open to changing their minds," he told the Senate Judiciary Committee.

In light of recent reports of government-authorized spying on U.S. soil without a court warrant, many Democrats want to make sure that if Alito is confirmed, he won't simply let slide executive branch attempts to override its authority.

"There is nothing more important for our republic than the rule of law," Alito said. "No person, no matter how high or powerful, is above the law and no person in this country is beneath the law."

Alito's comments came after he sat stoically for almost four hours on the first day of his confirmation hearing as Republican members of the committee attempted to back his record and Democrats described their wariness of his supposed views on everything from abortion to civil rights to executive power.

The hearing, which will last throughout the week, likely will be a more contentious one than that of Chief Justice John Roberts four months ago.

The committee's 18 members took turns giving 10-minute opening statements before Alito was introduced by his home state supporters, Sen. Frank Lautenberg, D-N.J., and former New Jersey Gov. Christine Todd Whitman, who worked for Bush in his first term. Alito introduced his family, including his wife, two children, in-laws, sister and cousins.

"When I had my confirmation hearing for the Court of Appeals, Philip was 3 years old," Alito said, referring to his son while offering the first glimpse of the demeanor he will attempt at the hearing. "And when I was called up to the chair, he took it upon himself to run up and sit next to me in case any hard questions came up."

Committee Chairman Sen. Arlen Specter, R-Pa., said Alito would be given "a full opportunity to address the concerns of 280 million Americans on probing questions that will be put to him by 18 senators representing their diverse constituencies.

"I have reserved my own vote on this nomination until the hearing is concluded. As chairman, I am committed to conducting a full, fair and dignified hearing. Hearings for a Supreme Court nominee should not have a political tilt for Republicans or Democrats. They should, in substantive fact and in perception, be for all Americans," Specter said.

Alito will give his opening statement before the panel breaks for the day; questioning resumes Tuesday. More than two-dozen officials from outside groups are expected to testify this week about their support and opposition to the nominee.

Dems: Alito's Burden is High

Specter said the hearing will give Alito a public forum to say his personal views will not interfere when deciding on issues relating to abortion and the 1973 Roe v. Wade decision that legalized abortion but that, "instead, he will weigh factors such as stare decisis on the precedents, women's (and men's, too) reliance on Roe, and whether Roe is embedded in the culture of our nation."

Sen. Patrick Leahy, the ranking Democrat on the committee, said he wants to be sure neither the Senate nor the Supreme Court should be a "rubber stamp" to White House policy.

"The challenge for Judge Alito in the course of these hearings is to demonstrate that he will protect the rights and liberties of all Americans and serve as an effective check on government overreaching," the Vermont senator said.

Sen. Charles Schumer, D-N.Y., told Alito that he has a triple burden to clear before he can be confirmed. That includes proving that he won't swing "the fulcrum of the court" to the right by replacing the moderate O'Connor and that he is more than just a darling of the conservatives.

"The same critics who called the president on the carpet for naming Harriet Miers have rolled out the red carpet for you, Judge Alito. We would be remiss if we did not explore why," Schumer said.

"Most importantly, though, your burden is high because of your record. Although I have not made up my mind, I have serious concerns about that record. ... You give the impression of being a meticulous legal navigator, but, in the end, you always seem to chart a rightward course."

Republicans have argued that the nominee cannot be forced to answer questions on issues that may come before him on the court; Democrats in the past have told more liberal judges like Ruth Bader Ginsburg that that same rule applies.

But Schumer argued that on issues such as abortion, which Alito has written about in the past, he cannot employ the so-called "Ginsburg rule" and refuse to answer some questions. Specter has said Alito has the right to be as brief as he wants in his answers.

Specter and Republican Sens. Orrin Hatch of Utah and Charles Grassley of Iowa bashed special-interest groups who they said are out of the "mainstream" and have been twisting and distorting the issues and cherry-picking certain decisions to characterize Alito's entire judicial philosophy in order to sway lawmakers one way or the other.

Sen. John Cornyn, R-Texas., said these groups are so vehemently opposing Alito because they can't get their initiatives passed at the ballot box and they're trying to get unelected judges in position who agree most with their points of view.

The Senate needs to rise above the battle raging between those groups, Hatch said.

"We must apply a judicial rather than a political standard to the information before us," he said. "I hope the days ahead will reflect more light than heat."

During remarks to reporters outside the White House Monday, Bush said Alito, who stood beside him after the two shared breakfast, has conducted himself with "dignity and class" leading up to the confirmation process.

"Sam's got the intellect necessary to bring a lot of class to that court. He's got a judicial temperament necessary to make sure that the court is a body that interprets the law and doesn't try to write the law," the president said. "I know the American people will be impressed, just like I have been impressed and a lot of other members of the Senate have been impressed.

Bush said he wants the Senate to conduct the hearings in the "dignified way" he said Alito deserves.

"The Supreme Court is a dignified body; Sam is a dignified person. And my hope, of course, is that the Senate bring dignity to the process and give this man a fair hearing and an up or down vote on the Senate floor," he added.

Abortion at the Top of Some Lists

Though Alito wrote two documents in the 1980s as a 3rd Circuit Court of Appeals judge that clearly demonstrate his opposition to abortion, as a judge, he has upheld existing law sometimes and has supported restrictions on abortion at others.

Filling O'Connor's seat is a "pivotal appointment," since she was the fifth vote on 148 cases, said Sen. Dianne Feinstein, D-Calif., telling Alito, "you well could be a very key and decisive vote."

"And so, during these hearings, I think it's fair for us to try to determine whether your legal reasoning is in the mainstream of American legal thought and whether you're going to follow the law regardless of your personal feelings on the law," Feinstein said. "I very much hope you will be straightforward with us — share your thinking and show your legal reasoning."

Sen. Lindsey Graham, R-S.C., said Alito's opinion on abortion rights shouldn't exclude him from getting an up-or-down vote. For example, Ginsburg, who was appointed to the high court by President Clinton, was openly pro-Roe and was confirmed by a vote of 96 to 3.

"If she came over in this atmosphere, she wouldn't get 96 votes," Graham said, adding that those in the "mainstream" include every Republican on the committee.

"We represent from the center line to the right ditch in our party and if all of us vote for you — you've got to be pretty mainstream … if every Republican member of the Judiciary Committee votes for you and you're not mainstream, it means we're not mainstream. It's a word that means anything you want it to mean," he said.

Graham said passionate feelings run on both sides of the issue.

"There are millions of Americans — a bunch of them in South Carolina — who are heartsick that millions of the unborn children have been sent to a certain death because of what judges have done," he said.

Grassley also pointed out that on some abortion rights rulings, Alito stuck to Supreme Court precedent rather than reinterpreting the law.

Aside from abortion, the scope of the executive branch of power and campaign finance reform — two big issues coming before the court shortly after Alito's confirmation vote — will also be examined. Other issues include: First Amendment rights guaranteeing freedom of speech and religion; Fourth Amendment rights relating to unreasonable search and seizure, warrants and probable cause; and the death penalty.

The issue of presidential powers is even more glaring since a frenzy erupted around Bush's authorization of the National Security Agency to eavesdrop without a warrant on American citizens talking with possible terrorists overseas.

The president's critics "are trying to make a case that President Bush is assuming more power than presidents over a long period of time have assumed ... and it's simply not true," said Grassley.

But Sen. Edward Kennedy, D-Mass., is skeptical of the president's agenda and Alito's purported deference toward it.

"In an era when the White House is abusing power, has authorized torture and is spying on American citizens, I find your support for an all-powerful executive branch and almost unlimited power for government agents to be deeply troubling," Kennedy said.

Alito has extensive experience as a government lawyer, prosecutor and judge. In 15 years as a judge on the 3rd Circuit Court of Appeals, he has voted 4,800 times in cases and written 361 opinions.

Click here for more information on Alito's opinions and other background material (pdf).

With that long list to choose from, "cases could be selected which would place him at any and every position on the judicial spectrum," Specter said.

"We all act like there's not an elephant in the room," said Sen. Joseph Biden, D-Del. "The truth of the matter is, there's significant debate among judicial scholars today about whether we've gone off the wrong path in regard to judicial decisions."

"Your record raises troubling questions about whether you appreciate the checks and balances in our Constitution — the careful efforts of our Founding Fathers to protect us from a government or a president determined to seize too much power over our lives," added Sen. Dick Durbin, D-Ill.

Cornyn said that on the issue of freedom of religion, "this country has gotten seriously off track" in that people aren't allowed freedom of expression when it comes to religion. He said to many Americans, it appears as if the court is more concerned about protecting pornographers than of this constitutional freedom.

Grassley said he will question Alito primarily on the 10th Amendment, or states' rights issues, the Commerce Clause and judicial restraint. Committee Democrats, including Feinstein and Schumer, have raised questions about Alito's argument that Congress can't legislate activities under the interstate Commerce Clause when the activities have nothing to do with interstate commerce.

Kennedy also said troubling aspects line Alito's record regarding civil rights and his commitment to "equal justice under the law."

"Alito's views of vast presidential authority and consistent rulings against individual citizens when up against the government, corporations, or other powerful interests raise questions of Alito's impartiality and commitment to equal justice," Kennedy said. "In Alito's 15-years on the bench, Judge Alito has not written one single opinion on the merits in favor of a person of color who alleged race discrimination in the workplace."

However, Sen. Jeff Sessions, R-Ala., pointed to two cases, in which Alito sided with minority plaintiffs.

"I would point him to U.S. v. Kithcart. There you made it clear the Constitution does not allow police officers to racially profile black drivers," Sessions said. "And they also may want to look at your majority opinion in Brinson v. Vaughn, where you ruled that the Constitution does not allow prosecutors to exclude African-Americans from jurors."

Grassley, who spoke right after Kennedy, said, "I have a much more positive view of Judge Alito," garnering a laugh before adding, "and I think the record will sustain my view."

Dropping The F-Word

Democrats have not ruled out the possibility of a nomination-ending filibuster, which would essentially prevent an up-or-down vote on Alito.

"No senator's vote, except for a declaration of war or authorization for the use of force, is as important as voting to confirm a United States Supreme Court nominee for a lifetime appointment," Specter said. "This is the quintessential example of separation of powers under our constitutional process as the president nominates, the Senate confirms or rejects and the successful nominee ascends the bench."

Those familiar with practice question-and-answer sessions say Alito has performed brilliantly but his weakest area has been on abortion-related issues.

Feinstein said she is prepared to filibuster Alito if she thinks he will overturn Roe v. Wade. Schumer also refused to rule out the possibility.

"I think you are hearing the word 'filibuster' because they are getting so much pressure from outside interest groups, whether the labor unions or pro-abortion groups or Ralph Nader type or civil rights. They are the base of the Democrat Party," Grassley said.

Cornyn said the question is, "how many of the 44 Democratic senators will acquiesce to special-interest groups who have provided a wealth of false allegations to discredit this fine nominee."

Democrats say they will not decide whether to filibuster or try to delay a committee vote until after the confirmation hearing ends.

If Democrats attempt a filibuster, Graham — a member of the bipartisan Gang of 14 that prevented implementation of the nuclear option, a Republican procedural move that would have stripped Democrats of the maneuver — said he will vote for Senate Majority Leader Bill Frist's decision to employ that option.

"I would consider that not only not an extraordinary circumstance, but a threat to the independence of the judiciary, and I would stop it in its tracks with my vote," he said.

Hatch earlier told FOX News that a Democrat-led filibuster over Alito not answering some questions would be "ridiculous."

"Regardless of what happens, it shows how ridiculously partisan this process has become," Hatch said. "That isn't the way it works. They [judges] have an obligation not to talk about future cases."

Asked if he would support the so-called nuclear option to prevent a filibuster, Hatch said, "You bet your life," calling the filibuster threat "a form of intimidation that really should not be a part of this process."

Specter has called for a Jan. 17 committee vote and Republican leaders want a full Senate vote on Jan. 20. Democrats have made no promises to stick to that schedule.

FOX News' Megyn Kendall and Liza Porteus and The Associated Press contributed to this report.