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"What we need to do is put them on a bus," said Ken Sowell, 63, a lawyer from Greenville, as he ate lunch recently at the diner. "We need to enforce the border. If they want to apply legally more power to them. I don't think just because a bunch of people violate the law, we ought to change the law for them."

Six years ago, the intensity of that kind of sentiment was enough to scuttle immigration overhaul efforts led by President George W. Bush and a bipartisan group of lawmakers, including Senators John McCain of Arizona and Lindsey Graham of South Carolina, both Republicans.

Now, as a new bipartisan group of eight senators, including Mr. Graham and Mr. McCain, try again — this time with President Obama as their partner in the White House — members of Congress will have to overcome deep-seated resistance like that expressed in the restaurant if they are to push legislation forward.

Republicans are betting that opposition from Tea Party activists and the party's most conservative supporters will have less impact because of the dire electoral consequences of continuing to take a hard line regarding immigrants. The senators on Monday released a blueprint for a new immigration policy that opens the door to possible citizenship ahead of a Tuesday speech on the subject by Mr. Obama in Las Vegas.

There is some evidence that the politics of immigration may be changing. Sean Hannity, the conservative host at Fox News, said days after the 2012 presidential election that he has "evolved" on immigration and now supports a comprehensive approach that could "get rid of" the issue for Republicans. Senator Marco Rubio of Florida, a rising star in the Republican Party, is pushing his own version of broad immigration changes — and getting praise from conservative icons like Grover Norquist and Ralph Reed.

But the Republican-controlled House remains a big hurdle. Speaker John A. Boehner on Monday was noncommittal about the emerging proposal, with a spokesman saying that Mr. Boehner "welcomes the work of leaders like Senator Rubio on this issue, and is looking forward to learning more about the proposal."

Representative Lamar Smith, Republican of Texas and a senior member of the Judiciary Committee, said that "when you legalize those who are in the country illegally, it costs taxpayers millions of dollars, costs American workers thousands of jobs and encourages more illegal immigration."

And if the lunch rush conversation at Tommy's is any indication, many Republican lawmakers will soon return home to find their constituents just as opposed to the idea as they were before. Concern about immigration varies regionally. But in many Congressional districts around the country, the prospect of intense opposition carries with it the threat of a primary challenger if Republican lawmakers stray too far from hawkish orthodoxy on the issue.

"The people who are coming across the border — as far as I'm concerned, they are common criminals," said Bill Storey, 68, a retired civil engineer from Greenville. "We should not adopt policies to reward them for coming into this country illegally. I have all the regard for them in the world if they come through the legal system, but not the illegal system."

Charlie Newton, a construction worker in the Greenville area, praised the work ethic of Hispanic co-workers, but said he opposes any laws that would provide benefits to illegal immigrants, including help becoming citizens.

"I think we need to help our own people before we keep helping somebody else," he said.

The president's proposals are expected to include more border enforcement, work site verification systems that allow employers to check the status of their employees online, and a road map to citizenship for the estimated 11 million illegal immigrants now living in the country. Democratic senators could begin work on a bill in the next couple of weeks.

In the Fourth Congressional District in South Carolina, which includes Greenville, the formal arrival of such a plan is likely to anger the constituents of Trey Gowdy, a Republican House member who was elected in the 2010 Tea Party wave and is now the chairman of a key subcommittee that will deal with immigration.

Mr. Gowdy has already taken a hard line, signing on last year to the "Prohibiting Backdoor Amnesty Act," which aimed to reverse Mr. Obama's plans to delay deportations for some young illegal immigrants. The congressman will be under pressure to change his mind from the White House and its allies, including groups like the U.S. Chamber of Commerce. But when he goes home to Greenville, Mr. Gowdy may find that his constituents want him to hold firm in his opposition.