Senate Minority Leader Mitch McConnell said Thursday that Republicans would not shut down the government in an effort to force President Barack Obama to repeal his health care law.

In an interview with CNN’s John King, the Kentucky lawmaker said Republicans will try to repeal it piece by piece, knowing that Obama will not sign on to a full repeal.

The Senator’s comments appeared to be the most definitive among statements by GOP leaders who have expressed an aversion to a shutdown. House Minority Leader John Boehner (R-Ohio), the presumed next Speaker, said before Tuesday’s midterm elections that a government shutdown was not his goal, but he said he would do “everything” he could to repeal the law. 

Rep. Steve King, one of the party’s most conservative lawmakers, has urged GOP leaders to attach a health care repeal to every spending bill once the party controls the House in the 112th Congress. The Iowa Republican wants the party to refuse to back down from repeal, even if a government shutdown ensues.

During Thursday’s interview, John King asked McConnell about comments he has made supporting House Republican efforts to defund implementation of the law. “Would you take that to the point of shutting down the government or not passing a budget, if that’s the only way to deny funding for the health care bill?” the television host asked, according to a transcript.

“No,” McConnell said. “I think we’re not talking about shutting down the government. What we’re — we’re doing here is talking about responding to the American people’s desire that this bill not become law. And my first choice, obviously, would be to put a full repeal on his desk. If we are unable to do that or if we are — were able to do it, he would certainly veto it. Then you come back and you go after it piece by piece.”

But he also said there are provisions in the health care law that should survive, including the ban on denying insurance to individuals with pre-existing conditions. “That’s one of the parts of the bill that everybody liked,” McConnell said.

He added that Republicans would target for repeal the law’s individual mandate to buy insurance, as well as its $500 billion in cuts to Medicare. “There are way more parts of this bill that are unfortunate and unpopular and should be done away with than a few portions of it that had pretty broad bipartisan support,” he said.

McConnell said in a speech Thursday that the party needs a Republican president elected in 2012 in order to accomplish all of its goals, including health care repeal.