In fact, several of them will have to confront an especially glaring paradox. Like Mr. Obama when he first ran for president, they are relatively young first-term senators, with limited experience beyond the country’s borders.

If the world’s unstable regions continue to dominate headlines in the next two years, some Republicans say they worry that their party’s nominee could have trouble persuading Americans to elect someone untested in international affairs.

“The potential for some unforeseen events is clearly going to create a great deal of unease,” said Richard G. Lugar, the former Republican senator from Indiana who led the Foreign Relations Committee twice, in the late 1980s and the mid-2000s. With so much unrest, Mr. Lugar said, Americans will inevitably ask themselves, “What if one of these Republicans became president? Would it be any better? Are they any better prepared?”

“And at the moment,” he added, “the answer is probably not.”

Unlike when the elder George Bush and John McCain won the Republican nomination in part because voters put trust in their foreign policy experience, the 2016 field is likely to be dominated by candidates who lack that background — senators who have been in office just a few years and governors who have had no exposure to the complexities of war and diplomacy.

Republican senators like Mr. Paul, 51, Mr. Cruz, 43, and Marco Rubio of Florida, also 43, could have an awkward case when arguing that they are better suited to address the world’s problems than Mr. Obama was when he was first elected. And while senators can point to their time in Washington as educational, the Republican governors who are weighing a White House bid, like Mr. Jindal and Chris Christie of New Jersey, have had limited global exposure.