GREENVILLE, S.C. — At Tommy’s Country Ham House, a popular spot downtown for politics and comfort food, not much has changed since 2007, the last time conservatives here made it crystal clear to politicians how they felt about what they see as amnesty for people who entered the country illegally.

“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.