Continued from page 1

The issue is tying the party in knots. Some Republicans warn that the party will pay a price in the 2014 elections if they use the power of the purse to force a government shutdown. Others, though, warn that they must draw a line in the sand during the spending debates this fall.

Perhaps nowhere are the political crosswinds more evident than in Kentucky, where Mr. Paul is backing Mr. McConnell’s campaign, although the incumbent — like Mr. Graham — has refused to sign on to the Senate conservatives’ pledge to oppose any funding to implement or enforce Obamacare.

Mr. Graham has said he wants to replace Obamacare but that he would not support a government shutdown because that would freeze Social Security payments and funding for the FBI and the military.

Mr. McConnell also is under fire from ForAmerica, a nonprofit conservative group led by Brent Bozell that is running an ad titled “Who Are the Biggest Chickens in Washington?”

The ad says Mr. McConnell has promised to fight to repeal Obamacare but loses his nerve when handed the chance to turn off the funding.

Sen. McConnell, conservatives don’t need a chicken when it comes to Obamacare,” the narrator says in the ad. “Leaders lead, but if you fund it, you own it.”

The effort also is causing friction between Republicans on the state and national level.

The New York Times reported Monday that Wisconsin Gov. Scott Walker, a likely 2016 presidential candidate, and some of the other governors at a National Governors Association meeting over the weekend in Milwaukee, warned against a spending showdown that could starve their states of money in the event of a shutdown.

“I have made the case that Obamacare is not good for the economy, but I have some real concerns about potentially doing something that would have a negative impact on the economy just for the short term — I think there are other ways to pursue this,” Mr. Walker told the paper.

Louisiana Gov. Bobby Jindal, who also is thought to be eying a White House bid, said he supports the defunding push.