McConnell can switch sides and move to reconsider the cloture vote. No notice needed, and he could also file a subsequent cloture motion, which sets in motion that delay before the next cloture vote. The delay in Senate Rule XXII is "one hour after the Senate meets on the following calendar day but one."
-- Would McConnell have the nerve to invoke the nuclear option AFTER a failed cloture vote --
If he has the nerve to invoke it at all, that would be as good a time as any. I'm sure Pence will be close by when the vote takes place.
Personally, I think the Democrat threat to filibuster Gorsuch is for show, to see how much they can get away with from McConnell.
In reality, Democrats know that the real fight is the next SCOTUS appointment. I read earlier reports suggesting that they want to keep the filibuster intact until then. Even if the nuclear option can be used even then, since the stakes will be higher when replacing Ginsburg, the MSM and Democrat furor over the nuclear option at that time will send McConnell catatonic if he shows any weakness now over what I believe is a filibuster bluff.
So the Schumer strategy should be to rattle and fray McConnell's nerves now, so that he's in a weakened mental state for the next fight.
-PJ