As many as three nights a week, Donald J. Trump has been hosting private dinners at Mar-a-Lago, schmoozing with some of the Republican Party’s biggest financiers as he races to address a sizable cash shortfall against President Biden.

There is no request for money from the attendees at these meals, which have included Larry Ellison, the billionaire co-founder of Oracle, and Pepe Fanjul, the sugar magnate, according to people familiar with the sessions. But advisers to Mr. Trump’s campaign and his super PACs hope the charm offensive will eventually pay political and financial dividends.

One of the most pressing issues facing Mr. Trump is the financial disparity he and allied groups now face with Mr. Biden and the Democratic Party. Mr. Biden’s campaign announced on Sunday that it entered March with $155 million cash on hand with the party, after raising $53 million in February. The Trump operation has not released a more recent total, but his campaign account and the Republican National Committee had around $40 million at the end of January.

Mr. Trump enters the general election ahead of Mr. Biden in public polls. But Mr. Biden has taken full advantage of one of the benefits of incumbency, both socking away cash and building out a political operation earlier than his challenger.

Despite years of professing massive wealth and boasting of his desire to “drain the swamp,” the deeply transactional former president is leaning yet again on the cash of others, turning Mar-a-Lago into a staging ground for billionaires and others with their own agendas. One potential leverage point with the biggest G.O.P. financiers is the package of tax cuts Mr. Trump signed into law in 2017. Many of those cuts expire at the end of 2025, and Mr. Biden has vowed not to extend them for the nation’s highest earners.

Money often winds up mattering less in presidential races than in down-ballot races. Voters pay attention to the candidates naturally, especially Mr. Trump, and the key states all wind up awash in advertising by the fall.