Story Highlights • Reid says Republicans do not support their own president's bill

• McConnell says many Republicans remain opposed to bill

• Lott says Bush won't sign just any bill and problems remain with it

• Bush visits Capitol to push immigration bill that was defeated last week



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WASHINGTON (CNN) -- President Bush broke bread with resistant Senate Republicans on Tuesday, but the fate of a White House-supported immigration bill remained uncertain.

After emerging from the private luncheon, Bush provided no specifics on whether any minds were changed.

"Some members in there believe we need to move a comprehensive bill, some don't," Bush told reporters in a Capitol hallway. "I understand that. It's a highly emotional issue. (Watch Bush press for passage )

"But those of us standing here believe now is the time to move to a comprehensive bill that enforces our borders and has good workplace enforcement, that doesn't grant automatic citizenship, that addresses this problem in a comprehensive way."

"I believe without the bill, it'll be harder to enforce our borders," Bush said. (Watch one Republican senator who remains unconvinced )

Senate Majority Leader Harry Reid, D-Nevada, said it's up to Republicans to collect more votes in favor of the measure to convince him that reviving debate could lead to passage.

"I repeat, 80 percent of the Democrats support this immigration bill," Reid said. "We've done our job. I don't have to twist an arm. I don't have to pull anybody into a room to get them to try to agree to something.

"It's not a question of Democrats doing anything. It's a question of Republicans supporting their own president." (Watch Reid challenge Republicans to come up with the votes )

If an agreement can be reached on amendments, Reid suggested, the Senate could return to the bill before the July 4 recess.

A motion to stop debate on the immigration measure failed Thursday night, preventing the proposal from coming up for a vote. Several Republicans wanted to add amendments, but Reid said the debate had gone on too long, and other bills were waiting to be considered. (Read more about last week's crushing blow to immigration legislation)

Seven Republicans voted with 37 Democrats and one independent in favor of the procedural motion that fell well shy of the 60 votes needed for passage. Fifty senators voted against it.

'Good give and take' at lunch

Senate Minority Leader Mitch McConnell, R-Kentucky, said there was "good give and take" at Tuesday's lunch, and sounded optimistic about the bill's chances.

"We didn't expect anybody to stand up and holler that they had an epiphany," McConnell said. "I do believe this bill is about 85 percent through to the finish line." (Watch why Bush's role is vital to immigration bill )

White House spokesman Tony Snow, appearing on CNN's "American Morning," said he expected Republicans to band together to add amendments to the bill, and predicted it could be voted on by the end of Tuesday -- after senators take up the energy bill. He predicted the measure would pass.

"What they didn't like last week is that the Senate Majority Leader Harry Reid wanted to cut off the debate, so a number of Republicans who had amendments they wanted to propose didn't get to have their hearing," Snow said.

Sen. Trent Lott, R-Mississippi, the minority whip, was less enthusiastic after the lunch meeting.

"The president made it clear to us that he won't sign just any bill. ... There are still problems remaining with it, and he wants to work with us to get this job done," Lott said.

Sen. Jeff Sessions, R-Alabama, also appearing on CNN's "American Morning" on Tuesday, said, "I think the president is wrong to push this piece of legislation so hard after we've demonstrated the flaws that are in it. He needs to back off. He needs to help us write a better bill and not push a bill that so many of us can't support." (Watch Sessions explain what he thinks is wrong with the 'fatally flawed' bill )

After lunch with Bush, Sessions told CNN he believes the bill has "serious flaws."

"I said we ought to back off and look at this thing carefully and analytically, because just passing a bill is not the solution to our problem," he said.

"If the president is not committed to actual aggressive enforcement and if we don't have a bill that will work, then we haven't done anything."

As examples, Sessions said, the Congressional Budget Office predicted only a 13 percent reduction in the number of illegal immigrants entering the United States if the bill passes, and the office would expect an increase in legal immigration.

Kennedy: 'The center is holding'

Before the luncheon, Sen. Edward Kennedy, D-Massachusetts, who worked with the White House and Republicans on writing the bill, issued a statement saying, "Like the president, many of us are very determined to get the job done and get it done now.

"The center is holding together: Last night we met to discuss the options for moving it forward, and today we'll continue that work. We share the sense of urgency that this important issue deserves."

Sen. Jon Kyl, R-Arizona, chief Republican architect of the immigration measure, said on "American Morning" that this is the last chance to pass legislation addressing the nation's 12 million illegal immigrants, about half of whom he said crossed into Arizona from Mexico.

"We have one good opportunity to pass immigration reform, and it's within the next few weeks in the U.S. Congress. I think all of the experts agree that thereafter we get into the presidential/political season. Next year it's not going to be possible," Kyl said. (Watch the signs that Bush is looking more like a 'lame duck' )

Sens. Johnny Isakson and Saxby Chambliss, Republicans from Georgia, sent a letter to Bush on Tuesday urging him to send an emergency supplemental spending bill to Congress to fund border security to restore "the confidence of the American people in the federal government's commitment to border security."

The immigration legislation would allow most of the illegal immigrants in the United States to qualify for a "Z" visa, to be renewed every two years; strengthen border security and enforcement; establish a temporary worker program for at least 200,000 people; fine employers who hire illegal immigrants; and create a new system for legal-resident ("green card") applications.

CNN's Ted Barrett and Steve Brusk contributed to this report.