Afterward, in a news conference, Mr. Paul admitted he still had a lot of work to do. Sometimes, he said, his audiences tell him: “I like what you’re saying. I’m still not voting for you.”

“That’s why you’ve got to keep saying it,” he said.

Mr. Paul’s remarks seem certain to stir up concern among Republicans over whether the senator — a libertarian-minded ophthalmologist who was first elected to public office three years ago — can appeal to the conservative voters who have so much influence in selecting the nominee.

He is not getting much support from Republican leaders in his efforts to change the discussion or the party’s tone. Colin L. Powell and Michael Steele, the former party chairman, have spoken against the restrictions. But no ranking Republican has done so, and there was no indication Friday that any would change their minds.

Senator Ted Cruz of Texas, often seen as a party rival to Mr. Paul, has said that it is unfortunate that it is “minority voters who are the victims of that fraud,” but that governments “should not be working to undermine the integrity of our elections.”

Another Republican widely seen as a contender for the party’s presidential nomination in 2016, Senator Marco Rubio of Florida, has embraced a contentious measure in his state to eliminate voting on Sunday and enact other restrictions.

Voting experts said the impact of the new laws might not become clear until the November elections. Many of the measures have yet to take effect, and a few will not start until 2016.

N.A.A.C.P. officials said they were encouraged that a prominent Republican would challenge his party. “But the proof is always in the pudding in terms of seeing exactly what policies and measures he might support as an elected official,” said Jotaka Eaddy, the group’s senior director of voting rights.