The latest signs of opposition to Ms. Vázquez, who is seen as too close to cover-ups and corruption in Mr. Rosselló’s unpopular administration, present a test for the new revolutionary movement that unseated the current governor: Can the loosely organized street protests that mobilized hundreds of thousands of people to oust Mr. Rosselló be channeled into longer-term change in Puerto Rico?

Protesters ran Mr. Rosselló out of office last week after the release of a series of offensive text messages tapped into longstanding public frustration over corruption, economic problems and a slow response to Hurricane Maria in 2017.

Emboldened by their victory, some of the leaders of the demonstrations are making it clear that their demands went beyond simply ending the governor’s term a year and a half early. They are insisting on fundamental democratic changes in a place where two-party politics have traditionally played out within a relatively limited circle of power. Fears that party leaders are negotiating secret deals to name a crony as the governor’s replacement — or that Ms. Vázquez could in fact end up as governor — have already led to the threat of ongoing protests.

[Read: 15 Days of Fury: How Puerto Rico’s Government Collapsed]

“It’s like they haven’t learned a thing,” said Melissa Mark-Viverito, a former New York City Council speaker whom the governor insulted in the chats and who has been participating in the protests. “For them to be striking back-room deals to pick a new governor is everything that the people found repugnant and everything that has the people marching again. You cannot replace one corrupt administration with another corrupt administration.”