Asst Prof Walid Jumblatt Abdullah, from Nanyang Technological University's (NTU) School of Social Sciences, said the party has little choice but to "drop her".
"She may decide to resign of her own accord, and that could work too. But either way, the party has to appear decisive in the wake of what happened," he added.
He noted the party's firm actions against former Hougang MP Yaw Shin Leong had helped it win the ensuing by-election.
Yaw was expelled by WP in 2012 for not upholding transparency and accountability when he failed to present himself to the party leadership and explain the allegations of extramarital affairs made against him.
"So I would not necessarily say that the party's credibility has taken a nosedive. How it reacts to this incident, however, will determine its credibility," said Prof Walid.
Raeesah had admitted on Monday to lying about a purported incident where she claimed the police mishandled a rape victim's complaint. The allegation was first made in Parliament in August.
Singapore Management University Assoc Prof Law Eugene Tan said the incident is more severe than what transpired last year.
While on the GE2020 campaign trail, Raeesah had to apologise for two Facebook posts she made alleging that the police discriminated against minorities. She was given a stern warning from the police over the matter.
Prof Tan said the party swiftly closed ranks then and apologised, which was a turning point in its election campaign, especially for Sengkang GRC.
"The elephant in the room is what did the WP leadership do when Ms Raeesah refused to substantiate her allegations against the police in the August sitting. We are talking about very serious allegations against the police," said Prof Tan.
"Furthermore, did they do enough by way of due diligence when Home Affairs Minister K. Shanmugam followed up on Ms Raeesah's allegations in the October sitting?
"The alarm bells should have been sounding loudly of Ms Raeesah's mea culpa."
Nydia Ngiow, managing director at strategic advisory consultancy BowerGroupAsia Singapore, said how WP handles this will also be a test for Leader of the Opposition Pritam Singh, the party's secretary general, and the rest of WP's leadership.
"This development has been a big blow to the credibility of the Workers' Party, given that her initial remarks, for which she did not even have the consent of the victim to share, cast doubt over the Singapore Police Force and wasted precious resources which could have been directed elsewhere," said Ngiow.
But the damage to the party's reputation is not insurmountable, added Dr Mustafa Izzuddin, who is a senior international affairs analyst with management consultancy Solaris Strategies Singapore.
"The WP ideological brand can outlive its current political predicament due to strong political leadership and solidarity in the party ranks, and there is sufficient time before the next election to turn around its current political quandary," he noted.
The observers said even if Raeesah leaves the party and vacates her position as MP for Sengkang GRC, a by-election is unlikely.
They added that the other three MPs - He Ting Ru, Louis Chua and Assoc Prof Jamus Lim - can still run the constituency.
Several of them also noted that a by-election was not triggered in 2017 when President Halimah Yacob stepped down from her position as MP for Marsiling-Yew Tee GRC to stand in the presidential election that year.
NTU political observer Felix Tan said that despite the incident, WP is likely to continue putting up younger candidates, including those working in non-governmental organisations.
But he added: "What this entire episode taught us is that this is a lesson for anyone who wants to be in politics. That what you say will be taken up to task.
"You will be questioned, you should be ready to answer them with facts and not hide behind the veneer of being young, of being in the opposition."