DEARBORN, Mich. — The second highest, hardest glass ceiling is pretty good too, right?

With the Democratic presidential nominee all but certain to be a man, party activists, elected officials and voters are setting their sights on the biggest consolation prize in American politics: the vice presidency.

Within hours of Senator Elizabeth Warren’s exit from the race, a departure that left the party facing a primary battle between two septuagenarian white men, prominent Democrats began publicly insisting that the ticket include a woman, preferably a black woman.

At least one women’s organization, Supermajority, circulated a petition asking both Senator Bernie Sanders and former Vice President Joseph R. Biden Jr. to “affirm their commitment to gender equity” by choosing a woman as their running mate. On Sunday, as he endorsed Mr. Sanders before thousands at a rally in Grand Rapids, Mich., the Rev. Jesse Jackson called for the next president to pick a black woman as vice president.

“There must be a woman on this ticket,” said Cecile Richards, a longtime abortion rights activist and a founder of Supermajority. “What is really important to see is representation, a commitment to the issues that women care about and a commitment to do something about it.”