The current logic is to use the phrase "just now" for time intervals less than four seconds in duration.
If it isn't too much trouble to implement, I think the user should just be allowed to accept the answer (the error message is not displayed) if the timer is within five seconds of expiring anyway.
Extra points for doing it this way on any timer that inhibits a user action (except for rate limiters like the timer to slow down posting of multiple comments).
