But Paul said he preferred a bill that "emphasizes border security first" and worried that if Republicans passed any bill in the House, a conference bill would ultimately resemble the Senate bill.

"What I would say is, the only way to avoid a problem with conference is for the Speaker of the House to say we are not going to conference and we will not allow a vote on anything coming out of conference that resembles a vote on the Senate bill," the Kentucky lawmaker said.

Last month, BoehnerJohn Andrew BoehnerBiden's relationship with top House Republican is frosty Maher chides Democrats: We 'suck the fun out of everything' Budowsky: Liz Cheney vs. conservatives in name only MORE said the push for immigration reform was "going pretty well" in the House, but he repeatedly emphasized he would not allow a vote on the Senate bill.

Paul also warned President Obama against taking military action in Syria without congressional approval.

"I don’t like the fact that the president thinks that he can just do what he pleases without Congressional approval on war, immigration, affordable care ... he seems to be going around the law," Paul said. "This is flat out wrong, and Congress needs to stand up and assert our authority and say to the president, 'You can’t do this. You are not a king' ".