WASHINGTON – Immigrant supporters claimed their first major victory since the Sept. 11 terrorist attacks after a bipartisan group of senators approved legislation that would give millions of illegal immigrants a chance at citizenship.

“It’s a big day for us. We may not have a lot of big days, but this is a big day,” Frank Sharry, executive director of the National Immigration Forum, a pro-immigrant group, said after the Senate Judiciary Committee approved a package of immigration and border security measures Monday.

Restaurant owners, agricultural groups, Democrats and others who had been pushing for a way for immigrants to earn legal permanent residency – the first step to citizenship – also claimed victory.

There was no immediate reaction from the White House, and Sen. Lindsey Graham, R-S.C., said he hoped President Bush, who advocates a so-called guest worker program, would participate in efforts to fashion consensus legislation.

Bush said he was determined to see some provision made on behalf of illegal immigrants who have been working in this country.

“Don’t underestimate me,” Bush told Mexican and Canadian reporters in an interview Monday. He said that no one should discount his ability to get a new immigration bill from Congress despite his struggles with lawmakers in the past year.

The next step is the full Senate, where Majority Leader Bill Frist, R-Tenn., is negotiating with other senators on how to handle the committee’s bill and his own proposal, which focuses more on punishing employers who hire undocumented workers.

“The situation along our southern borders now ranks as a national security challenge, second only to the war on terror,” Frist said Monday. “Every day thousands of people violate our frontiers.”

Frist said the Senate will begin a debate on immigration later this week with the aim of passing a bill by April 7.

The debate will give Americans a glimpse of two candidates for the Republican presidential nomination in 2008: Frist and Sen. John McCain, R-Ariz., an architect of the bill approved by the Judiciary Committee.

McCain said the turnouts in the hundreds of thousands – particularly among Hispanics – at recent rallies in Los Angeles, Chicago and Washington helped galvanize support for the bill.

“I’d like to point out that a lot of these young people are children and grandchildren of people who came here illegally who are citizens themselves who don’t want their grandmother sent back to Guadalajara,” McCain said Tuesday on ABC’s “Good Morning America.”

McCain acknowledged that there were “sharp divisions” within the Republican Party over the approach to illegal immigration.

Despite Bush’s support for letting illegal immigrants with jobs avoid deportation, many Republicans vow to prevent what they say amounts to amnesty from becoming law.

Any bill produced by the Senate would also have to be reconciled with the get-tough House bill, which would make illegal immigrants felons.

In general, the Judiciary Committee’s bill is designed to strengthen enforcement of U.S. borders, regulate the flow into the country of guest workers and determine the legal future of the estimated 11 million immigrants living in the United States illegally.

The bill would double the Border Patrol and authorize a “virtual wall” of unmanned vehicles, cameras and sensors to monitor the U.S.-Mexico border.

It also would allow more visas for nurses and agriculture workers, and shelter humanitarian organizations from prosecution if they provide non-emergency assistance to illegal residents.

The most contentious provision would permit illegal aliens currently in the country to apply for citizenship without first having to return home, a process that would take at least six years.

They would have to pay a fine, learn English, study American civics, demonstrate they had paid their taxes and take their place behind other applicants for citizenship, according to aides to Kennedy, D-Mass., who was instrumental in drafting the legislation.

Kennedy credited the “faith community” for building support for a guest worker program.