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To understand the kind of re-election battle Representative Dana Rohrabacher is facing, take a look at a billboard overlooking Newport Boulevard in Costa Mesa. Larger-than-life images of Mr. Rohrabacher and President Trump face a quote attributed to Kevin McCarthy, the House majority leader: “There are two people I think Putin pays: Rohrabacher and Trump.”

Mr. Rohrabacher’s relationship with Russia is again under scrutiny. On Tuesday, he said that he had met with Maria Butina, who was indicted on charges of conspiracy and acting as a foreign agent, on a 2015 trip to Russia. But Mr. Rohrabacher dismissed the charges against her as “bogus.”

And a day earlier, he gave the most enthusiastic defense of the president’s remarks in Helsinki.

Mr. Rohrabacher’s close ties to Russia have provoked criticism from politicians even in his own party. And Democrats hope his support for the Kremlin will help lead to his defeat this November. But it is unclear whether that support will become a central issue in the campaign. Several voters in the district said they saw the outrage as a side issue propped up by Democrats.

“He’s a good man who shares our values,” said Sandra Leach, 77, a Laguna Beach resident. “I don’t follow every twist and turn in this hunt, but I think it’s a bunch of politics driving it. We can’t become a socialist country with open borders.”