House Homeland Security Committee Chairman Rep. Michael McCaul (R-Texas) said Sunday that Americans don't want comprehensive immigration reform, and instead prefer a piecemeal approach.

"They don't want a comprehensive bill like what we saw with Obamacare," McCaul said on CBS's "Face The Nation," adding later: "What they want is regular order pieces of legislation."

Rep. Xavier Becerra (D-Calif.) disagreed. "If the machine is broken, you've got lots of broken parts. If you fix one part, it doesn't mean the machine is going to work well," he said on the same program.

McCaul, whose border security bill passed out of his committee, called the sweeping bill the Senate recently passed "not a responsible plan."

The House GOP Conference will meet Wednesday to discuss immigration. Rep. Raul Labarador (R-Idaho) said that if Republicans do not approach the issue of immigration correctly, it could mean the end of the GOP.

"I actually think that if we don't do it right politically it's going to be the death of the Republican Party," he said on NBC's "Meet The Press." "If we do it right, I think it's going to be good for us."