Senate Minority Leader Mitch McConnell told a crowd at a health care forum in Kentucky on Tuesday that while he does not like the president’s health care law, shutting down the government over funding it “will not stop” it from existing.

“I’m for stopping Obamacare, but shutting down the government will not stop Obamacare,” McConnell told the audience at Baptist Health Corbin, according to a WYMT-TV reporter at the event.

Several conservative senators — including Ted Cruz of Texas, Mike Lee of Utah and Marco Rubio of Florida — have said the GOP should not vote to fund the government unless they can stop money from flowing to Obamacare. Of course, the effort is likely to go nowhere, given that the Democratic-controlled Senate would never approve such a measure and President Barack Obama certainly would never sign it into law.

Other Republicans have opposed trying to use such a maneuver for exactly that reason.

Sen. Richard M. Burr, R-N.C., even called a shutdown over the health care law the “dumbest idea” he’d ever heard of. But for McConnell to hint that he might not support to the tea party-backed effort is a bit of a surprise. He has recently tended to publicly back pushes from the more conservative wing of his party, particularly those championed by fellow Kentuckian Rand Paul, and he is facing a tea party-inspired primary challenge.

The political dangers of a government shutdown showdown are very real for Republicans, and that McConnell would imply that, to constituents at home, demonstrates how problematic this particular divide in the party is.