WASHINGTON - A conservative group is launching a radio ad challenging Senate Republican leader Mitch McConnell to oppose any money for President Barack Obama's health care law even if it means triggering a government shutdown.

The Senate Conservatives Fund is spending nearly $50,000 on the 60-second commercial that will begin airing on Tuesday in Kentucky, where McConnell is locked in a tough race for a sixth term. The GOP leader faces both a primary rival, businessman Matt Bevin, and a Democratic foe, Secretary of State Alison Lundergan Grimes.

"Republicans in Congress can stop Obamacare by refusing to fund it, but Senator Mitch McConnell refuses to lead the fight," says the ad which also makes a reference to a recent campaign embarrassment for McConnell.

"The Obamacare bill stinks, and holding your nose won't make it any better," the commercial says.

Earlier this month, audio of a Jan. 9 telephone conversation revealed that Jesse Benton, McConnell's campaign manager, said he was "holding my nose" while working for the candidate. Benton later said in a statement that he believes in McConnell and is 100 percent committed to his re-election.

The Associated Press obtained a text of the conservative group's ad in advance.

The Senate Conservatives Fund, which was founded by former South Carolina Republican Sen. Jim DeMint, is spending close to $200,000 on radio ads in six other states calling on GOP senators to refuse to fund the health care law. The group's targets are North Carolina's Richard Burr, South Carolina's Lindsey Graham, Lamar Alexander of Tennessee, Johnny Isakson of Georgia, Mississippi's Thad Cochran and Arizona's Jeff Flake.

The issue has divided Republicans, with House and Senate GOP leaders wary of the political impact of any government shutdown but tea party conservatives determined to undermine the health care law.

The federal 2013 fiscal year ends Sept. 30. New money must be appropriated by then to avoid a shutdown of countless government offices and agencies.

The radio ad comes as another conservative group, the Madison Project, launched a radio spot on Monday critical of McConnell, labeling him a "career Washington politician" who claims to be a conservative. The Madison Project is supporting Bevin's candidacy.

The Senate Conservatives Fund has not endorsed in the Kentucky GOP primary, but in a statement in July, executive director Matt Hoskins said the group was open to backing Bevin. Hoskins said McConnell could lose the Senate race and cost the GOP its shot at the Senate majority.

The group said it was "waiting to see if the grassroots in Kentucky unite" behind Bevin.