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The momentum that helped carry the massive immigration overhaul through the Senate last month is beginning to fade, as House Republicans slam the brakes on the debate while rejecting the Senate’s bill entirely.

The discontent in the House Republican caucus was evident in a closed-door meeting late Wednesday. Cheers erupted when GOP leaders said they would not take up the Senate-passed bill.

“One thing is clear. House Republicans want to do this on our terms and not on the Senate’s terms and not on the president’s terms,” said Rep. Michael McCaul, R-Texas, chairman of the House Homeland Security Committee.

Senate leaders, who had been banking on the assumption that political pressures would force the House to act, are now watching as the House weighs options that would be a direct challenge to those who crafted the original bill.