There has to be some mechanism -- I guess ultimately the courts -- that would require the Dems to deal the vote.
A legislative body can't ignore it's own rules.
I doubt any suits will be filed. The House and Senate each write their own rules. As crazy as it seems, no law was broken.
It is a political problem and will be handled in a political fashion. One way perhaps would be for the GOP to not attend any further House business until the rats rescind the bill they sent to the Senate.
Doing nothing on the part of the GOP should not be an option.