Mr. Van Drew, who hails from a Republican-leaning district that for 24 years before his election was represented by a Republican, is one of only two Democrats who voted against rules laying out the impeachment process.

Mr. Van Drew has not spoken publicly since reports emerged over the weekend that he was switching parties. But in an interview with Tucker Carlson on Fox News several weeks ago, Mr. Van Drew said Mr. Trump would likely survive an impeachment process given Republican control of the Senate and that voters, not Congress, should decide Mr. Trump’s fate.

“At the end of the day, I’m afraid all we’re going to have is a failed impeachment,” he said, adding: “The bottom line is he’s still going to be the president of the United States, and the bottom line is he is still going to be the candidate of the Republican Party. So why don’t we let the people do the impeachment by voting in the electoral process the way that we usually do.”

Senior advisers to Mr. Trump have assured Mr. Van Drew that he would have the president’s support in the primary.

The Trump campaign declined to comment on Monday. But Mr. Trump praised Mr. Van Drew on Sunday on Twitter. “Always heard Jeff is very smart!” the president wrote.

Assemblyman Jon Bramnick, a Republican who is the minority leader said, “I’ll take as many new Republicans as I can get in New Jersey.”