The Senate will begin debate on immigration reform Tuesday afternoon after the Senate Judiciary Committee wrapped up a bill that addresses the concerns of many illegal immigrants and border patrol hawks.

But that bill isn't to the liking of Senate Majority Leader Bill Frist, who is expected to open debate on his own piece of legislation. Frist argues his version is a "strong border security bill which addresses most immediate problems that we have."

It's expected that the first amendment to be tacked on to Frist's bill will be the alternative bill reported out of the Senate Judiciary Committee on Monday night. After eight hours of debate, the panel passed a reform bill on a 12-6 vote

"All Americans wanted fairness and they got it this evening," said Sen. Edward Kennedy, the Massachusetts Democrat who was a key coordinator of the bill.

On several amendments, GOP Sens. Lindsey Graham of South Carolina, Sam Brownback of Kansas and Mike DeWine of Ohio, who is seeking re-election this fall, sided with Democrats. Committee Chairman Arlen Specter, R-Pa., also voted for the bill though he signaled that some of the provisions could well be changed by the full Senate.

In fact, many of the provisions that passed are in great jeopardy since the legislation was approved without a majority of Republicans' support. Before the panel vote, Frist said if the committee didn't finish its work before midnight, he would bring his own border security-only bill to the floor. Now that it has passed with fewer than half of the committee's 10 Republicans supporting it, Frist plans to ignore the panel's final product and continue with his own legislation.

The majority leader's measure would punish employers who hire illegal immigrants and provide more visas. It sidesteps the issue of whether to let illegal immigrants already here stay, though he says he opposes that idea.

"I am a little disappointed in (the committee bill) because I think it is going to be characterized as amnesty in the sense that it adopted provisions late this afternoon that does not require people who have been here illegally to go back to their native countries before (they) apply for green cards before applying for citizenship," Frist told FOX News.

In a Monday radio interview with Tony Snow on "FOX News Talks," Frist said he thought it is impractical to have a fence thousands of miles long, along the U.S.-Mexico border. Frist said his bill would include a "virtual wall."

"In some areas it would be a triple-fence wall, but in some you may have unmanned aerial vehicles, infrared censors, physical monitoring," he said.

Aides to Specter, Kennedy, as well as to Republican Sens. John Cornyn of Texas, Jon Kyl of Arizona and John McCain of Arizona, who is not on the Judiciary Committee — spent much of last week trying to find a compromise that would stave off Frist's bill.

Senate Democrats have threatened to filibuster Frist's bill because they want a measure that address more comprehensive reforms.

"We have a train wreck waiting to happen," one Senate Republican source told FOX News.

Many Exceptions Made for Illegals

The Judiciary Committee bill includes several victories demanded by demonstrators on Capitol Hill who urged the Senate to reject new get-tough measures on the estimated 11 million illegal aliens currently in the country. Among them, the committee rejected a House move to change illegal border crossings from a misdemeanor to a felony.

"The House made that violation a felony and I want to be clear I don't agree with that and I don't know anyone on the committee who agrees with that," said Cornyn.

The committee also moved to protect churches and charities from House language that protesters feared could lead to the arrest of Samaritans who help illegal aliens.

"A priest who counsels an undocumented mother to stay in the United States with her U.S. citizen children rather than abandoning them could be subject to this criminal penalty," said Sen. Dick Durbin, D-Ill.

Rep. James Sensenbrenner, R-Wis., chairman of the House Judiciary Committee and author of the House bill, said the House bill is aimed at alien smugglers, not people trying to give honest assistance to illegals in the United States.

"I am disappointed by the erroneous accusations lodged against the strong House-passed border security bill aimed at preventing illegal immigration that I sponsored," Sensenbrenner said.

"I would hope everyone would embrace a good-faith effort to combat alien smuggling gangs rather than engage in fear-mongering that clergy and good Samaritans will be thrown in jail. That's absolutely false and beneath the level of dialogue this important issue deserves," he added.

The Senate committee rejected a proposal by Cornyn to require humanitarian groups providing food, medical aid and advice to illegal immigrants to register with the Department of Homeland Security. In December, the House voted to make offers of non-emergency aid a felony.

Kennedy, who crafted much of the legislation with McCain, prevailed on a proposal to allow an additional 400,000 green cards for future immigrants, regardless of the industry where they find jobs. Sen. Dianne Feinstein, D-Calif., won approval on an 11-5 vote for a five-year program to permit as many as 1.5 million agriculture workers into the country. They will be allowed to seek permanent legal residence.

"It will provide the agriculture industry with a legal work force and offer agriculture workers a path to citizenship," she said.

The committee approved more than doubling the current force of 11,300 Border Patrol agents in an effort to stem the tide of new undocumented workers arriving daily. It voted to add 2,000 agents next year and 2,400 more annually through 2011. The bill also authorizes a "virtual wall" along the U.S.-Mexico border that consists of actual fences as well as unmanned vehicles, cameras and censors.

Kyl, who sponsored his own bill with Cornyn, warned that the bill as it is written will die before it's law.

"If the bottom line is that all of the people who came here illegally have got to be made citizens, then we may as well have the vote right now. You all may have the votes to pass that, but it will never become law. I'll vote against it, that's amnesty, that's not going to work," he said.

Bush Prefers Guest Worker Program

President Bush says no one should discount his ability to get a new immigration law from Congress, despite his struggles with lawmakers in the past year. The president wants lawmakers to pass a guest worker program that would let many illegal immigrants already in the United States stay for six years if they have jobs and have stayed out of criminal trouble.

Many Republicans say that's unacceptable and nothing short of amnesty.

"Don't underestimate me," Bush said Monday in an interview with Canadian and Mexican reporters, saying his ideas is "a humane way to deal with people who are making a contribution to our economy."

He added: "I am disgusted by a system in which people are snuck across the border in the bottom of an 18-wheeler … There's a more humane way to deal with our neighborhood."

Thousands of immigration advocates rallied Monday at the U.S. Capitol, where dozens of members of the clergy wore handcuffs to protest what they say is the House bill's criminalization of their aid programs for poor immigrants. More protests were expected Tuesday.

Employers and immigration advocates prefer the plan offered by Kennedy and McCain to Frist's. The Kennedy-McCain measure would allow illegal immigrants to become eligible for permanent residency after working for six years. Both McCain and Frist are likely candidates for the Republican presidential nomination next year.

Some are wary of such bills and say they're basically amnesty for people who are in the United States illegally.

"The McCain-Kennedy-Specter bill that came out of the Judiciary Committee today provides nearly universal amnesty for the more than 12 million illegal aliens in the U.S. The bill also adds hundreds of thousands of foreign workers to a background check system that is already on the brink of collapse. The Judiciary Committee even adopted Durbin’s amendment, which reduces penalties so that visa overstays will continue to undermine our immigration system," said Rep. Tom Tancredo, R-Colo., one of the chief House hawks on illegal immigration.

Anything but a requirement for illegal immigrants to return home amounts to amnesty, Kyl argued.

"Well over 60 percent of Americans in all the polls I see think it's OK to have temporary workers, but you do not have to make them citizens," said Kyl, who is seeking re-election this fall.

FOX News' Major Garrett and Liza Porteus and The Associated Press contributed to this report.