The White House earlier this month announced it would delay implementation of the ObamaCare employer mandate, which requires businesses to provide healthcare to employees or pay fines. The administration said the decision gave businesses time to comply, but Republicans said it highlighted that the entire health law was unworkable, with some questioning the constitutionality of the delay.

Cotton said that move mad him wary of backing immigration reform efforts.

"ObamaCare is his namesake, landmark legislation that he desperately wants to be effective,” he said of the president. “If we pass immigration legislation that legalizes first and then has enforcement later, why would he ever enforce the provisions of the law related to enforcement, whether it's the border fence, whether it's the visa tracking system, whether it's an employment verification system? 

“He will just decide, 'You know what? We're not going to enforce it,'" said Cotton.

Cotton's comments come as the House takes center stage in the debate over overhauling the nation's immigration system. 

Last month the Senate passed a bipartisan immigration bill offering a pathway to citizenship for illegal immigrants already in the country and more enforcement measures, including doubling the length of border fencing and the number of patrol agents along the U.S.-Mexico border.

“The Senate bill is, I believe, amnesty first and enforcement later," Cotton said. 

Speaker John BoehnerJohn Andrew BoehnerAre maskless House members scofflaws? Israel, Democrats and the problem of the Middle East Joe Crowley to register as lobbyist for recording artists MORE (R-Ohio) has said the Senate bill is a nonstarter, and House conservatives are pressing for a bill that does more on border security before beginning to legalize the status of illegal immigrants.

"What I would like the House to do is a discrete, piece-by-piece approach to immigration that builds confidence of the American people that we actually and finally will secure our border and enforce our immigration laws," Cotton said.

A report in National Review said that Cotton had become a leading conservative voice on immigration reform, urging a piecemeal approach that prioritizes border security. 

Cotton on Monday dismissed suggestions in that report that his push on immigration reform was motivated by a possible challenge to Sen. Mark PryorMark Lunsford PryorBottom line Everybody wants Joe Manchin Cotton glides to reelection in Arkansas MORE (D-Ark.).

"I really haven't had a chance to think about it," Cotton said of a possible Senate bid. "But one of these days we will."