In January, the law firm of the powerful Democratic lawyer Marc Elias launched a gambit intended to help his party.

The Elias Law Group petitioned the Federal Election Commission to allow a George Soros-funded political action committee to coordinate with Democratic campaigns and party committees in Texas to get out the vote to defeat Republicans, whom Mr. Elias accused of anti-democratic voter suppression.

The request was approved by the F.E.C. in an advisory opinion in March.

In a turnabout, it was quickly seized on by former President Donald J. Trump’s campaign, which began working with groups funded by billionaires like Elon Musk on a canvassing operation targeting swing state voters in the final days of the campaign.

“We’ll know soon whether it was genius or lunacy to put all this in Elon Musk’s hands, but it’s bad that you can do it at all,” said Tom Moore, who until last year served as chief of staff for a Democratic member of the F.E.C. who opposed the request. “Opening the money faucets up as wide as they go strikes me as a bad idea for Democrats, because Republicans just have a bigger faucet.”

In his three-decade career, Mr. Elias has arguably done more than any single person outside government to shape the Democratic Party and the rules under which all campaigns and elections in the United States are conducted. He and his firm have been retained by Vice President Harris’s campaign to assist with recounts and anticipated legal fights after the election.

His efforts have earned him an enthusiastic fan base among Democrats and anti-Trump Republicans, who see him as a heroic bulwark against democratic backsliding, and have celebrated his wins, including two significant Supreme Court rulings last year.