WASHINGTON — It started as a scrappy grass-roots protest movement against President Trump, but now the so-called resistance is attracting six- and seven-figure checks from major liberal donors, posing an insurgent challenge to some of the left’s most venerable institutions — and the Democratic Party itself.

The jockeying between groups, donors and operatives for cash and turf is occurring mostly behind the scenes. But it has grown acrimonious at times, with upstarts complaining they are being boxed out by a liberal establishment that they say enables the sort of Democratic timidity that paved the way for the Trump presidency.

The tug of war — more than the lingering squabbles between supporters of Hillary Clinton and Senator Bernie Sanders of Vermont — foreshadows a once-in-a-generation reorganization of the American left that could dictate the tactics and ideology of the Democratic Party for years to come. If the newcomers prevail, they could pull the party further to the left, leading it to embrace policy positions like those advocated by Mr. Sanders, including single-payer health care and free tuition at public colleges.

The upending of the left comes amid a broader realignment in American politics, with the Republican Party establishment also contending with a rising rebellion, driven by pro-Trump populists. Just as the new forces on the right are threatening primary challenges to establishment Republicans, some groups on the left have begun talking about targeting Democratic incumbents in the 2018 midterm elections.