It is one of the most potent and feared weapons in the arsenal of modern American politics: the super PAC.

But as three dozen Democrats ponder presidential runs in 2020 and begin to design their campaign infrastructures, some leading names beyond Senator Bernie Sanders are expected to forgo or disavow these fund-raising committees that allow allies to haul unlimited sums from wealthy backers. The hope of these potential candidates is that grass-roots donors and progressive activists would reward them more handsomely in the primary for rejecting such funds.

If she runs, Senator Elizabeth Warren of Massachusetts is likely to reject the assistance of a super PAC, according to two people familiar with her thinking. And the former Vice President Joseph R. Biden Jr. revealed in a little-noticed passage in his 2017 book that he would have gone without one if he had run in 2016, making it more difficult for him to backtrack now.

The question is a politically vexing one. The financial firepower would be alluring to those with a ready network of financiers, such as Senator Cory Booker of New Jersey, who is seen as likely to have a super PAC, according to donors, strategists and people close to him. Some allies are already discussing possible super PACs for Senators Kamala Harris of California and Kirsten Gillibrand of New York, the two most Democratic donor-rich states in the nation. But aides to both of them say they are not currently seeking these fund-raising vehicles.