Immigration reform is one of the issues topping the list for Congress as it heads back to work after the Fourth of July holiday.
Many conservative House members don't like the new Senate immigration bill, passed with the help of Republicans, which provides a pathway to citizenship for millions of immigrants who entered the country illegally.
On the Sunday talk shows this weekend, they used the word "concern" more than once.
"My concern with the Senate bill is that they put the legalization of 11 million people ahead of security," Rep. Raul Labrador, R-Idaho, told NBC's "Meet the Press."
"The legalization happens first, and then the security happens second. And I think the American people are not going to stand for that," Labrador said.
But others in the GOP are arguing for consensus. Arizona Sen. John McCain is one of the so-called "Gang of Eight" Republican and Democratic senators who wrote the immigration bill.
He said on CBS "Face the Nation" that the Senate is ready to work with the House and that he trusts the leadership of Speaker John Boehner.
"I believe that if they can come up with a bill, we would be more than eager to negotiate with them. A failure to act is de facto amnesty for 11 million people living in the shadows," McCain cautioned.
"I think, wherever you are on that issue there's agreement on that. So then, shouldn't we sit down together and solve this issue, not only for the good of the Republican party but for the good of the nation?" he asked.
But a large number of House Republicans are not willing to hand Democrats a political victory while passing what they see as a bad law.
House Homeland Security Committee Chairman Michael McCaul, R-Texas, also used the word, "concerned" on "Face the Nation."
He urged that the efforts to protect the country's borders be bipartisan. He expressed uneasiness that the process of crafting a bill could be maneuvered to help the Democrats politically.
"Border security on my committee was a unanimously approved, completely bipartisan bill," McCaul said.
"My concern is the political backdrop could be that the White House would like to see this fail in the House so (the president) can blame the House of Representatives for that and then try to take back the House of Representatives and all bets are off on his agenda," he said.
House members heard from their constituents over the weeklong Fourth of July break, and will meet privately Wednesday to determine their strategy.
Leaders say it may be at least September before lawmakers take final action.