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Instead, he said that Congress should take a piecemeal approach to the problem, starting with stemming the flow of illegal immigrants into the country.

Only then, Mr. Rubio said, will there be the political will to deal with the millions of illegal immigrants already living here.

Meanwhile, in the wake of the war in Gaza, which has fueled a strong response from the party’s deep pool of pro-Israel voices, Mr. Paul has tried to reassure voters that he has never supported cutting aid to Israel, despite previous statements to the contrary.

While opponents use flip-flops to attack candidates, Michael McKenna, a GOP consultant, said they also show the political process is working.

“These shifts are part of what makes popular sovereignty so great — those who want to get elected have to (ultimately) express the will of the majority of the electorate, or they don’t get elected,” Mr. McKenna said in an email. “And usually people like to do it when not too many folks are watching the evolution. Because it can get misconstrued as being indecisive or, worse, pandering.”