Rosselló has promised to step down at 5 p.m. Friday in response to huge street protests by Puerto Ricans outraged at corruption, mismanagement and an obscenity-laced chat that was leaked in which the governor and 11 male allies made fun of women, gay people and victims of Hurricane Maria.
"It's frustrating. We're in limbo," said Jose Ramos, a taxi driver. "The island doesn't have a path forward."
As one of his last acts, Rosselló put forward veteran politician and lawyer Pedro Pierluisi to fill the vacant secretary of state post, next in line for the governorship under the U.S. territory's constitution.
Pierluisi is a former representative to the U.S. Congress seen by most ordinary Puerto Ricans as a conciliatory, relatively uncontroversial figure, unlikely to be met by continued street demonstrations.
"I offered to take a step forward for Puerto Rico at this moment given my love for my country," Pierluisi said. "My only loyalty as governor, if I have the support of legislators, is to the people of Puerto Rico.
The Puerto Rican House of Representatives is expected to vote on Pierluisi's confirmation Friday afternoon. If he is rejected, Justice Secretary Wanda Vázquez automatically becomes governor as the next in the order of succession, even though she has said she would unwillingly accept the job.
Some lawmakers said a House vote for Pierluisi would count as confirmation and allow him to assume the governorship. Opponents said he requires Senate approval, too, and they would sue to stop him becoming governor without that.
"The situation could not be more complicated," said Sen. José Antonio Vargas Vidot, an independent. "This is absurd, what we're going through. We never thought something like this could happen."
Rep. Rafael Hernández, a leader among opposition legislators, said he believes a "yes" vote by the House for Pierluisi on Friday would mean Vázquez becomes governor at 5 p.m. and Pierluisi her secretary of state.
He said he would sue to stop any attempt to make Pierluisi governor, throwing the island into even more uncertainty.
"We would go to the courts early Saturday or Friday afternoon," he said. "Anything can happen."
Another obstacle for Pierluisi is Senate President Thomas Rivera Schatz, who has said he would not vote for Rosselló's nominee and wants to run for governor himself next year. Several legislators have said they prefer Rivera Schatz over Pierluisi, but the Senate leader is a powerful figure deeply associated with Puerto Rico's political and business elite and his elevation to the governorship could re-ignite popular outrage.
Rivera Schatz delivered a scathing attack on his critics Thursday afternoon and said the Senate would hold a hearing on Pierluisi on Monday.
"Let's give him the chance to defend himself," Rivera Schatz said. "I don't think I'm going to be convinced."
He criticized Pierluisi for being an attorney with the law firm that represents the federal control board overseeing the island government's finances, calling it "Puerto Rico's No. 1 enemy."
Rosselló's New Progressive Party holds majorities in both chambers of the legislature, meaning a united party could have easily named the next governor.
Many Puerto Rican legislators were predicting that Pierluisi did not have the votes to be confirmed.
But Rep. Gabriel Rodríguez Aguiló of the governing party said that an overwhelming number of constituents had called to ask for his confirmation.
"We ran out of paper," he said in reference to secretaries taking notes on the calls.
After jubilation at the success of their uprising against Rosselló, Puerto Rican protesters have been frustrated at the political infighting and paralysis that has followed.
Some lawmakers joined Rivera Schatz in complaining about Pierluisi's work for the law firm representing the control board, which was created by Congress to oversee Puerto Rico's finances before the territory, saddled with more than $70 billion in public debt, declared a form of bankruptcy. Pierluisi's brother-in-law also heads the board, which has clashed repeatedly with Rosselló and other elected officials over demands for austerity measures.
"That's a serious conflict of interest," Rep. José Enrique Meléndez told The Associated Press.
Sen. Eduardo Bhatia of the opposition Popular Democratic Party, accused Rivera Schatz of trying to maneuver himself into the top job.
"This attitude of (Rivera Schatz) taking the island hostage is very dangerous," Bhatia tweeted. "'It's him or no one' is in keeping with what has been a life silencing and destroying democracy."
Puerto Rico's 3.2 million people are U.S. citizens who can't vote for president and don't have a voting representative in Congress. While politicians are members of the Democratic or Republican parties, the island's main political dividing line is between Rosselló's statehood-favoring party and the Popular Democratic Party, which favors a looser association with the federal government. Both parties' memberships contain a mix of Democrats and Republicans.
More than a dozen officials have resigned in the wake of the chat that drove Rosselló from office, including former Secretary of State Luis Rivera Marín.
Pierluisi, who took a leave of absence from the law firm, said in a statement Wednesday that much work remains to be done to recover the trust of federal authorities, Congress and the people of Puerto Rico as it also struggles to recover from Hurricane Maria.
Pierluisi represented Puerto Rico in Congress from 2009 to 2017 and then ran against Rosselló in the 2016 primaries and lost. He also previously served as justice secretary under Rosselló's father, Pedro Rosselló, when he was governor.