Now that former President Donald J. Trump is a convicted criminal, the Democratic Party finds itself wrestling with a choice that will help define this year’s presidential race: Should it try to push his felonies to the center of the election?

The route Democrats take may determine not only Mr. Biden’s fortunes but also, they say, the future of American democracy. Widely believing a vengeful Mr. Trump poses a grave threat to the nation, Democrats at all levels of the party are simultaneously thrilled to see him found guilty and fearful that he has a supernatural ability to survive even this political peril.

Post-verdict interviews with more than 50 Democrats — including current and former members of Congress, statewide elected officials, veteran strategists, Democratic National Committee members and local officials — revealed a party hungry to tell voters that Mr. Trump’s conviction makes him unfit and worried that Mr. Biden might not use the bully pulpit of the presidency to press that argument.

“I do think it is the obligation of every Democrat to remind every voter that Donald Trump is now a convicted felon and just how unprecedented this is,” said former Representative Beto O’Rourke of Texas, a Democrat who ran for the presidential nomination against Mr. Biden in 2020.

Even as Democrats broadly push Mr. Biden to capitalize on Mr. Trump’s felonies, there is a spectrum of opinion on just how much to focus on them.

Mr. Biden himself has deployed a two-pronged strategy, speaking carefully about Mr. Trump’s legal problems even as his campaign grows more aggressive: On Friday evening, it fired off an evening statement that referred, for the first time, to “Convicted Felon Donald Trump.”