Things don't have to be as messy as they appear to be on the opposition side. Even if they are disunited, all that is needed is for different parties to act rationally in their own best interest. The facts are not too difficult to grasp. Workers' Party contested in the SMC with decent results in the 2011 elections. Riding the moral high ground after the recent AIMgate and Palm-gate, it's chance of winning is very good and it is not reasonable to expect Workers' Party to give up this opportunity to take up one more seat to add to the pressure it has put on the PAP on various issues. The recent proposal by SDP[Link] for WP not to participate in the by-election is ludicrous and self-damaging - they lost some of the credibility they gained during GE2011....the best thing they can do now is not to make things worse for themselves by joining a contest they will certainly lose due to lack of time to work the ground and be blamed for causing the loss of a seat that could have been won by another opposition party. Unfortunately, based on what they have done in recent days, I'm not sure if they are able to stop damaging their own reputation further.
"But given the mood change since, the ruling party will have a tougher time – if it is a two-party contest. If it faces the Workers Party alone, the PAP may likely lose." - Seah Chiang Nee[Link]
We start off with a roughly 50-50 situation in a direct contest between WP and PAP. You can't say for sure who will win because it is hard to assess the swing votes but we know the swing will be in favor of WP because Palmer was far better known than Dr. Koh and things have not gotten better (for Punggol residents and Singaporeans) since the 2011 election. Starting with this, any additional opposition party that comes in to contest will chip away WP's block of votes - the irony is the better quality their candidate, the bigger chunk they will take and the less likely an opposition candidate will win the seat.
Chiam See Tong's party SPP and NSP have chosen to do the sensible thing to stay out of this contest. These are the 2 parties that came closest to winning parliament seats in GE2011 after the WP - with narrow defeats in Potong Pasir and Marine Parade GRC.
For the other parties, whatever their intentions are, their joining the contest will stop the WP from winning another seat without gaining anything but blame for helping the PAP retain its seat in Punggol East. Opposition supporters will be left with this feeling of "what could have been" and morn a wasted opportunity. We saw the end result of vote splitting in the Presidential Election, it is likely that Tan Cheng Bock would have won if the votes were not split. But nobody could have foreseen this close fight between Tan Cheng Bock and Tony Tan - you cannot blame the other presidential candidates for the missed opportunity because it was unpredictable. However, for this by election, we have baseline results from GE2011 so there is no excuse to hand PAP the victory by splitting the votes when the people of Punggol East actually want an opposition member of parliament.
To put it simply, the PAP will win in a 3- or 4- corner fight. The opposition parties joining the contest will walk off as losers - a defeat they inflict on themselves. Unless their goal is to stop the WP which they see as a rival, the decision to contest just makes no sense. If they are there to stop the WP, then these other parties are led by people whose intentions are not very clear. A stronger WP will pave the way for other opposition parties. The better WP performs, the stronger the proof that alternatives to PAP can perform well and that will help people to overcome their reservations about voting for alternatives. Other parties can choose to leverage on the success of WP to advance their own cause or they choose to turn this win-win situation into a lose-lose one. Perhaps, the biggest obstacle to the progress of opposition politics is not the PAP - these days they can't seem to solve any of our problems and reverse the rising discontent- but the inability of personalities in opposition parties to make sensible decisions.