"This is a vital debate," Mr. Bush said in a statement on the White House South Lawn. "I thank the members who are working hard to get a bill done. I strongly urge them to come to a conclusion as quickly as possible and pass a comprehensive bill."
The president said he wants legislation "that will cause the people in the interior of this country to recognize and enforce the laws and a bill that will enable us to have a guest-worker program that will recognize that there are people here working hard in jobs that Americans don't want."
The Senate is seriously stuck on this immigration issue and working towards a Friday deadline for the start of a two-week spring break.
It is conservatives in the president's own party blocking a bill that would set up a guest-worker program, reports CBS News correspondent Bob Fuss. And with their threatened filibuster, there aren't the 60 votes needed right now for any version. Leaders are looking for compromise but having a very hard time finding common ground between those who would make illegal immigrants legal and those who want them all kicked out.
Democrats set up a Senate floor showdown over a proposal that would allow the illegal immigrants to remain in the country and become permanent residents after paying $2,000 fines and back taxes, learning English and working six years.
"Are the Republicans going to stand up for comprehensive immigration reform or not?" Sen. Dick Durbin, D-Ill., asked Tuesday.
Republicans had floated a proposal Monday night and early Tuesday to divide illegal immigrants between those who have been in the country more than five years and those who have not.
Several rank-and-file Republicans objected, and Majority Leader Bill Frist and fellow Republicans spent much of the day trying to find an alternative.
"I don't know that we're going to get a bill," said Sen. Mike DeWine, R-Ohio. "It's tough."
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.
Durbin 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."