The competitive, divisive primary that many Democrats long wanted to avoid has arrived anyway — playing out largely behind closed doors in a fight over the bottom of the ticket.

The final stage of the campaign to be Vice President Kamala Harris’s running mate reached something of an ugly phase in recent days as donors, interest groups and political rivals from the party’s moderate and progressive wings lobbied for their preferred candidates and passed around memos debating the contenders’ political weaknesses with key demographics.

They turned most sharply on one of the favorites to join the ticket, Gov. Josh Shapiro of Pennsylvania, who has drawn opposition from progressives and even a senator in his home state.

The fissures among Democrats emerged as three leading contenders — Mr. Shapiro, Senator Mark Kelly of Arizona and Gov. Tim Walz of Minnesota — met with Ms. Harris at her residence in Washington on Sunday, ahead of a decision her campaign said would be announced by Tuesday.

Kevin Munoz, a spokesman for the Harris campaign, declined to comment on the Sunday meetings.

Ms. Harris is set to hit the campaign trail with her running mate this week, kicking off a five-day, seven-state tour with a Tuesday night rally in Philadelphia, where Mr. Shapiro is expected to be in attendance, whether he is her pick or not.

Progressive groups have trained their criticisms on Mr. Shapiro and Mr. Kelly, who they accuse of being too conservative on key issues. Shawn Fain, the head of the United Autoworkers Union, said during a Sunday interview on CBS that Mr. Kelly had “not really” assuaged the union’s concerns about his commitment to pro-labor legislation and that the organization had “bigger issues” with Mr. Shapiro’s support for school vouchers.