No. No time limit, but...
If you do not progress all the love interests equally, it may do 2 things:
1. Prevent later events for some characters from triggering (if you skip anyone due to dislike for any reason) and...
2. Have events that talk about or refer to things you have not yet experienced with other characters.
We have combed through countless times to try and playtest every update, to ensure this does not happen... but being a sandbox environment, it's still probable people will waste time grinding cash (which you do not need to do at all) or find a single pivotal character not to your taste and avoid them, causing the above 2 possibilities.
In general, everything up through 0.12.2 should happen within approximately 150 days... Unless you try to grind money.
Publicly available cheat code for $10k cash: Greedisgood
(case sensitive - so capitalize the G)