"There are not votes in the House to pass the Senate bill," Bishop said, according to the Deseret News. "It should not be passed under any condition. Either do it right or you don't do it at all."

But he rejected the idea that the conversation in Washington has become to shrill to get anything done on immigration.

"I don't hear the language as more shrill at all," he said. "I hear the language as more accommodating than ever before. You hear that more as a media point of view than it is reality."

To the contrary, he said House Republicans are simply insisting that border security is handled first, including by giving border patrol agents access to environmentally protected lands. Bishop has proposed legislation to give these agents more access to this land, which he said would be better than building a bigger fence.

Bishop said the chances of passing these sorts of reforms are "decent." But he acknowledged that it's now clear what the House can support on the issue of how to handle illegal immigrants already in the country.

The Senate's bill would create a pathway to citizenship for these people, but the House has yet to consider any language on that issue.