WASHINGTON (AP) – Conservative Republicans tweaked their alternative to a bipartisan guest worker proposal for illegal immigrants Wednesday as Democrats pressed for a vote that would put most of those in the U.S. illegally on a path to citizenship. President Bush urged swift action.

The latest counterproposal to a bill by Sens. John McCain, R-Ariz., and Edward M. Kennedy, D-Mass., would base the chance of citizenship for the estimated 11 million illegal immigrants in the U.S. largely on whether or not they were here before a cutoff date. That date has not yet been determined.

Those in the U.S. before the cutoff date, an overwhelming majority, could apply for green cards if they pay fines and back taxes and learn English. Among that group, those who had spent five years in the U.S. would get an easier path to citizenship, with newer arrivals facing more obstacles.

Those who arrived illegally after the cutoff date would be viewed as living here illegally and unlikely to qualify for citizenship while in the country.

“There has to be some cutoff date. They would not have a status,” said Sen. Sam Brownback, R-Kan.

Kennedy’s and McCain’s measure would put immigrants here before Jan. 7, 2004, on a path toward citizenship if they maintain jobs and meet the other conditions.

Bush said the immigration bill should include a guest worker provision that allows illegal immigrants to remain in the United States to perform jobs that, he said, Americans will not perform. But he said the legislation should not include an amnesty provision that provides automatic citizenship.

He called on the Senate “to come to a conclusion as quickly as possible and pass a comprehensive bill.”

The McCain-Kennedy bill has heavy Democratic backing and some Republican support. But enough Republicans consider it amnesty that they could block a vote on it.

“I don’t know that we’re going to get a bill,” said Sen. Mike DeWine, R-Ohio. “It’s tough.”

Democrats have rejected previous compromise offers and gave no immediate indication that they would endorse the latest one. Sen. Harry Reid of Nevada, the Democratic leader, blocked numerous attempts by Republicans to hold votes Tuesday on selected amendments. “We do not need a compromise. It’s in our bill,” he said and later set the stage for a test vote on Thursday.

Democrats need 60 votes to overcome objections from conservatives on the immigration bill approved by the Senate Judiciary Committee that is being pushed by Reid.

Sen. Dick Durbin, D-Ill., acknowledged the votes to cut off debate and force a final vote are not there, but said Democrats had to move because they feared Frist was going to let the clock expire on the bill, in its second week on the floor.

But Republicans blamed Democrats for inaction. “The other side is delaying, postponing, obstructing and not allowing votes on amendments,” Frist said.

The House has passed a bill that would shore up border security by putting the military on the border, requiring employer to verify they’ve hired legal workers and making being in the country illegally a felony.

A strong Senate bill would mean a better bargaining position in conference committee with the House, Durbin said.

The White House repeated President Bush’s call for a temporary worker plan as a way to identify the millions of illegal immigrants in the country. The administration said in a statement it wants a bill that does not create “an automatic path to citizenship.”