House Republican Deputy Whip Peter Roskam (R-Ill.) said Thursday morning that the Senate immigration bill likely won't come to a vote in the House, labeling it a "pipe dream."

“The House has no capacity to move that bill in its entirety,” he told a breakfast hosted by the National Review. “It just won’t happen. It is a pipe dream to think that bill is going to go to the floor and be voted on.”

The Senate bill is primed to get the support of less-than one-third of Senate Republicans on Thursday. In the House, most bills require the support of a majority of Republicans, under the so-called "Hastert Rule," and the House GOP conference is notably more conservative than the Senate GOP caucus.

House GOP leaders have said -- and Roskam repeated Thursday -- that the House will move forward with its own immigration bill, potentially sending the Senate and House versions to a conference committee to work out a final package that would need to be approved by both chambers.

Roskam left open the possibility that the House version would include a path to citizenship for illegal immigrants -- a cornerstone of the comprehensive Senate bill which Democrats insist on -- but that it would only come with sufficient border security.

”Once there is a level of confidence on a secure border, then you can begin to move forward on these other elements,” he said.