The combined efforts of these groups, along with the shift of rank-and-file Republicans toward hawkishness, could isolate Mr. Paul. This will be most vividly apparent once debates begin this year. With Republican candidates increasingly attacking Mr. Obama for what they see as his unwillingness to project American strength, Mr. Paul’s support for the administration’s policies on such issues as negotiations with Iran over its nuclear program will stand out — and force him into some awkward situations.

“You’re not going to find any of the Republicans, even those who might well have behaved like Obama, standing up and defending Obama,” said Richard Perle, a pro-interventionist defense official who served in the Reagan administration.

The movement of Republican public opinion is striking. In 2009, worn down by the long and unpopular Iraq war undertaken by Mr. Bush, about 53 percent of Republicans said the United States should “mind its own business” internationally and let other countries get along the best they can on their own, according to a Pew Research Center survey.

But the shocking images of terrorism and Mr. Obama’s approach to them have set off much concern among Republican voters, said Senator Kelly Ayotte, Republican of New Hampshire. Ms. Ayotte recalled that, after she spoke at a recent party dinner in her home state, Republican activists had approached her to discuss the threat of the Islamic State and the Obama administration’s nuclear negotiations with Iran.

“National security issues have really risen to the top in the presidential race, and that’s because of what we’ve seen happening around the world and in part because of the ineffective policies of this administration,” Ms. Ayotte said.

Even last week, as former Gov. Jeb Bush of Florida sought to distance himself from his brother’s foreign policy record at a speech in Chicago, he found himself embracing the sort of muscular engagement that had characterized the 43rd president’s administration.

The former Florida governor called nonstate terrorist groups such as the Islamic State “perhaps the greatest security threat that we now face for our own homeland.”