A test comes on April 25, when Spencer Zwick, the national finance chairman for Mitt Romney’s presidential campaigns, is slated to introduce top donors in Boston to Mr. Paul. While some fundraisers say Mr. Paul’s resistance to the use of military force abroad disqualifies him from leading the GOP, others are intrigued by his efforts to grow the party by reaching out to young and minority audiences.

Support from donors who backed Mr. Romney, a defense hawk, would provide more evidence that Republicans are coming to favor a more restrained U.S. military role. Wall Street Journal/NBC News polling this year shows that members of each party in nearly equal numbers would look less favorably, rather than more favorably, on a candidate who believes the U.S. should do more to resolve conflicts around the world…

The strategy has a cost. “A lot of tea partiers were going against the grain when they supported Rand in 2010, and now he’s turned his back on the movement in a lot of people’s opinions,” said Andrew Schachtner, president of the Louisville Tea Party, which is backing Mr. McConnell’s challenger, Matt Bevin. “Tea partiers aren’t much for balancing acts.”

Mr. Paul has tried to mitigate the fallout by praising Mr. Bevin as a “good, honest Christian man” and championing issues dear to Kentucky libertarians, with Mr. McConnell’s help. A provision to allow the economically strapped state to try hemp farming was inserted into the farm bill. The two senators have introduced right-to-work legislation that would forbid labor contracts that require employees to pay union dues. Mr. McConnell has also signed on to Mr. Paul’s proposal to expand oversight of the Federal Reserve.