Like the October 1996 Lautenberg Abomination (which IIRC passed with veto-proof margins in both House and Senate)?
Well sort of. I was actually thinking of the Original AWB, which was an amendment to a what was originally a House bill. The amendment, which started life as a "free standing" bill just like the ones currently filed, didn't pass the Senate at midnight, but rather November 17, 1993, at 10:10 AM. (That may have been when the voting started rather than when it finished) Of course the bill had to go back to a conferance committe and be re-voted on by each House. Some of that may have occurred in the wee small hours, for example the final Senate Vote on the conference report was August 25, 1994, 10:24 PM, with the final House vote the day before, 21-AUG-1994 7:51 PM. It's hard reconstruct some of the votes and actions from information available on "thomas".
I would expect that if either of the current "renewal" bills, or any renewal bill, makes it into law, it will be as part of some big "must pass" bill, since that gives a certain amount of "deniability" to the CongressCritters, especially those from the house that did not attach the provisions to the larger bill. Then as now, the Senate contains a higher fraction of "RKBA hostile" types, so it would seem likely this stuff would follow a similar path. Probably attached to anti-terrorism legislation rather than anti-crime as before.