South Korean President Park Geun-hye’s conditional resignation offer appears to be causing cracks in what previously had been a strong push for her impeachment, with opponents now struggling to set a date for a vote to strip her of power.

Park offered on Tuesday to leave office if parliament arranged a safe transfer of power, triggering an immediate backlash from opposition parties, which called the overture a stalling tactic to help the president navigate a huge political scandal involving a shadowy confidante.

Leaders of the country’s three main opposition parties met on Wednesday and agreed to stick with their plan to try to vote on an impeachment motion as early as Friday.

But they also said they’d meet again if that plan does not work, meaning they’re bracing for the possibility that a Friday vote might not take place.

“In handing over the decision of her fate to the national assembly, Park Geun-hye has essentially allowed the national assembly to really squabble over the details of how her eventual removal from office should take place,” Al Jazeera’s Harry Fawcett said, reporting from Seoul.

“The ruling party, the Saenuri Party of Park Geun-hye, came out earlier on Thursday saying unanimously that the members wanted her to see President Park step down by the end of April, and that the new presidential election should take place by the end of June.

“However, the anti-Park camp within that ruling party is saying that if, by next week if there isn’t an agreement between the opposition and ruling parties on such a process, then they still will vote with the opposition at the end of next week for an impeachment process.”

Much of their hesitation to pick a clear date is due to the fact that there are not enough opposition lawmakers to pass an impeachment through parliament, and they would need help from dissenters in Park’s Saenuri Party.

READ MORE: South Korean opposition moves to impeach President Park

The three opposition parties and anti-Park independent lawmakers have a total of 172 seats in the 300-seat National Assembly. A passage of an impeachment motion requires at least 200 votes in favor. About 40 ruling party lawmakers have expressed their willingness to vote to oust Park.

But after Park’s resignation offer on Tuesday, made in an address to the nation, anti-Park lawmakers gathered and agreed it would be best for Park to resign in April, after the installation of a neutral Cabinet that can help ensure a stable power transfer until a new president is elected, according to the office of Hwang Young-cheul, one of the lawmakers who attended the meeting.

They said they would still take part in a possible impeachment vote on Dec. 9 if details for an April resignation aren’t worked out through negotiations, Hwang’s office said.

Opposition parties have previously said a vote on Park’s impeachment would take place either on Friday or Dec. 9, because parliamentary plenary sessions are already scheduled on those days.

“It’s true that some cracks have taken place at anti-Park forces in the Saenuri Party after her speech,” said an official at the main opposition Democratic Party, formerly known by its Korean-language name, Minjoo.

The official, who requested anonymity because he wasn’t authorized to speak to the media, said opposition parties are using unofficial, backroom channels to see if they can still secure enough Saenuri lawmakers who would align with their impeachment drive.

If impeached, Park’s presidential powers would be suspended until the Constitutional Court makes a ruling on her fate. The court would have 180 days to deliberate.

Park, in her Tuesday speech, continued to deny accusations by prosecutors that she colluded in the criminal activities of her longtime friend Choi Soon-sil, who, despite having no official role in government, allegedly had a say in policy decisions and exploited her presidential ties to bully companies into giving large sums of money to businesses and foundations that Choi controlled.

READ MORE: South Korea’s political morass

Prosecutors have indicted Choi, two ex-presidential officials and a music video director known as a Choi associate for extortion, leaking confidential documents and other charges.

The scandal has sparked mass protests every Saturday in Seoul. About 30,000 anti-Park demonstrators gathered in the city’s downtown area on Wednesday, according to protest organizers.

Park, who has immunity from prosecution while in office, has refused to meet with prosecutors. She has, however, agreed to undergo questioning by a special prosecutor.

On Wednesday, she picked a special prosecutor among the two candidates recommended by opposition parties. The special prosecutor has 120 days to lead an independent investigation into the scandal.

“I will only focus on truth as I investigate,” Park Young-soo, the special prosecutor, told reporters. “I will not be distracted by the circumstances and thoroughly investigate (the case) based on law and principle.”