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Supreme Court nominee Harriet Miers (search) continued to try to garner support from senators on Capitol Hill Wednesday while some conservative groups questioned her nomination.

Republicans who helped ensure a smooth confirmation process for John Roberts (search), President Bush’s pick for Supreme Court chief justice, are now causing tension in the party with concerns that Miers isn’t conservative enough.

"I'm getting reports on both sides," said Paul Weyrich (search), a conservative leader from the Free Congress Foundation. "Some people are quite enthused about her and other people are very upset. The grass-roots are not happy, I can tell you that."

Sen. Trent Lott, R-Miss., said Wednesday that it's not enough for a president to say "trust me" when it comes to the highest court in the land.

"There are a lot more people -- men, women and minorities -- that are more qualified in my opinion by their experience than she is," the former Senate majority leader said in a television interview. "I don't just automatically salute or take a deep bow anytime a nominee is sent up ... I have to find out who these people are, and right now, I'm not satisfied with what I know."

White House spokesman Scott McClellan (search) on Wednesday said the nomination still fresh and suggested that there would be more support for Miers after senators looked "at her record of accomplishment."

McClellan said Miers would answer senators’ questions during confirmation hearings but the White House would not release “confidential deliberative documents” relating to her work for the president.

But before confirmation hearings begin, Miers is doing all she can to be accessible to senators and give them a better idea of who she is and what kind of justice she would be in replacing retiring Justice Sandra Day O’Connor (search).

Democrats say they want to find out more about the 60-year-old nominee, who met with Sen. Patrick Leahy (search), the top Judiciary Committee Democrat from Vermont, on Wednesday.

Leahy has not announced how he will vote on Miers' nomination, saying, "it is too early to reach any firm judgement about such an important nomination."

Senate Minority Leader Harry Reid said so far, so good, but has not given indication of whether he would vote for Miers. He added that the addition of a justice with years of experience as a practicing lawyer would benefit the court.

"With so much at stake, we shouldn't rush to judgment about this or any other nominee, but even at this early stage of the confirmation process, I will say that I am impressed by what I know about Harriet Miers," Reid said.

Miers also met Wednesday with Sen. John Cornyn (search), R-Texas, who known her for 15 years.

Cornyn vowed to support Miers’ nomination and urged colleagues to do the same.

“I don’t need to reserve judgment because I know she’s the right person for the job now,” said Cornyn, who served as a type of informal spokesperson for Roberts during that nominee's confirmation process.

But the former Texas judge acknowledged that Miers faces problems from some conservatives. "The president in a sense has disarmed some of his critics, but also made some of his supporters nervous by this nomination," Cornyn said.

Meanwhile, Miers’ nomination is drawing scrutiny, praise and criticism from different groups, as more details about her background and life come to light.

"President Bush has an excellent record of appointing judges who recognize the proper role of the courts, which is to interpret the law according to its actual text, and not to legislate from the bench," said David N. O'Steen, executive director of the National Right to Life Committee. "We believe that Harriet Miers is another nominee who will abide by the text and history of the Constitution.

Feminist Majority Foundation President Eleanor Smeal told FOX News that Bush’s nomination offers no paper trail for the Senate to investigate and will create a burden on expediting the confirmation process.

“He nominated a person without a paper trail, a stealth candidate,” Smeal said.

Anti-abortion group Operation: Rescue on Tuesday promised an active campaign to get Bush to withdraw her nomination.

"The president seems to do what is politically expedient, versus what is morally correct," said Troy Newman, leader of Operation: Rescue. "Therefore, if we make it politically expedient for him to do the moral thing, that's what he'll do."

Roberta Combs, president of the Christian Coalition, said: "I trust that she will be an excellent addition to the high court and all Americans will be proud of her."

Sandy Rios, former president of the Concerned Women for America, said she hopes Miers will be confirmed quickly to allow more focus on the war in Iraq.

Rios said the recent stories on Miers’ born-again Christian faith will help her on the bench.

“It is a good thing that Harriet has faith and something beyond herself,” Rios said.

Texas Supreme Court Justice Nathan Hecht (search), a friend of Miers, said the nominee has many strengths and will rule on the bench fairly.

“When you become a judge and you take that oath, you promise to look at cases on their merits and not substitute your personal views for the rule of law,” Hecht told FOX News.

During a Rose Garden press conference Tuesday, Bush said Miers was a woman of great character and “an extraordinary woman.”

“I know her heart,” Bush said. “Her philosophy won’t change.”

The president repeatedly told reporters that he was confident in his choice, implying that conservatives should back the nomination.

While reporters inquire about Miers’ position on abortion, Bush said he doesn’t recall ever talking to her about that issue.

FOX News contributor Marvin Kalb (search), a lecturer at Harvard University’s John F. Kennedy School of Government, said the White House is battling criticism, realizing that Miers’ nomination requires a major effort to push through.

“This is one of the greatest challenges facing this particular president,” Kalb said. “This is the beginning of a major effort by the White House. Everybody has to chip in. This is a major offensive in which the media plays a big role.”

But other Senate conservatives haven’t stepped forward to pledge support for Miers.

"There's precious little to go on and a deep concern that this would be a Souter-type candidate," said Sen. Sam Brownback (search), a Judiciary Committee Republican and a possible 2008 presidential candidate, referring to Supreme Court Justice David Souter (search), nominated by former President Bush and later surprised supporters when he showed liberal tendencies on the court.

"The circumstances seem to be very similar," said Brownback, who will meet with Miers on Thursday. "Not much track record, people vouching for her, yet indications of a different thought pattern earlier in life."

FOX News' Greg Kelly and the Associated Press contributed to this report.