Congressional Republicans pressed ahead Sunday with their emerging stance on immigration reform, arguing President Obama delaying the implementation of his health care law raises major concerns about whether he’ll enforce border security measures in immigration laws.

“We cannot fix with laws things the president refuses to do,” Iowa Republican Rep. Steve King told “Fox News Sunday.”

Though well known as one the House’s most conservative members, King has emerged as perhaps the chamber’s most vocal opponent of the Senate’s immigration bill, which includes $40 billion toward additional security along the U.S.-Mexico border and a path to citizenship for at least some of the roughly 11 million illegal immigrants now living in the United States.

House Republicans appeared to emerge with the new strategy after a closed-door meeting Wednesday, which was preceded by the Obama administration saying earlier this month that it will delay the start of the so-called employer mandate part of the president’s signature health care law until after the 2014 elections.

“If the president can selectively enforce ObamaCare, what’s to say he cannot selectively enforce border security?” House Majority Leader Eric Cantor said ahead of the meeting.

New York Democratic Rep. Steve Israel urged King and other House members opposed to existing immigration reform legislation not to use the president’s delay on ObamaCare -- and arguments his administration currently doesn’t enforce border security -- to block immigration reform.

“You shouldn’t use this as an excuse,” he told Fox News, pointing out 68 of the Senate’s 100 members agreed this summer to reform legislation and that President George W. Bush and the majority of Americans want the federal government to fix the country’s broken immigration system.

He also said Democrats would work with House Republicans if they wanted to approach immigration reform by passing the legislation in pieces.

King also argued Sunday that it was a “mistake” to think the 2012 presidential election in which Obama won roughly 71 percent of the Hispanic vote was a referendum on immigration.

Democrats want immigration for a “political issue,” he said.