"Amnesty is wrong in any circumstance, and if we are going to fix our broken immigration system--and we should--it makes much more sense to do so next year, so that we are negotiating a responsible solution with a Republican Senate majority rather than with Chuck Schumer," Cruz said in a statement to Breitbart.
Cruz said he thinks any distraction from Republican talking points on Obamacare could hurt the party in the election.
"Anyone pushing an amnesty bill right now should go ahead and put a 'Harry Reid for Majority Leader' bumper sticker on their car, because that will be the likely effect if Republicans refuse to listen to the American people and foolishly change the subject from Obamacare to amnesty," he said.
The Texas senator added that a bill that includes "amnesty" could keep conservative voter away from the polls.
"Republicans are poised for an historic election this fall--a conservative tidal wave much like 2010. The biggest thing we could do to mess that up would be if the House passed an amnesty bill--or any bill perceived as an amnesty bill--that demoralized voters going into November," he said. "Amnesty will ensure they stay home."
Cruz has a history of urging members of the House Republican conference to join him in his push to repeal Obamacare. During the government shutdown in October, Cruz met with some of the most conservative members of the House about his effort to repeal the law, to the dismay of some Republicans in the Senate.