Essentially their excuse would be that senate rules allow republicans all kind of stalling measures. For example, requiring 60 votes for any cloture vote and then mandating 30 hours of "debate" after the bill has already achieved cloture, plus other procedural "holds" and blocking moves which stall weeks from other priorities, and they're finally now able to get around to this. Republicans have been routinely blocking every bill as long as possible and wasting 30 hours of time after every bill passes.
If the democrats had any spine they'd use the nuclear option though, Which would basically be involve saying "The constitution says a majority governs the senate, so we have 51 votes here to ignore everything the republicans say" then they'd give the republicans the middle finger and pass whatever they want with their 51 votes. Republicans could take it to court and we'd see who wins. The problem is the democrats probably don't have 51 votes for that even if harry reid supported it... there are a lot of "democrats" who are basically bought off and would find an excuse not to let that happen. So the senate is now basically where good bills go to die (if this is indeed a good bill, admittedly i haven't researched the details on this particular bill.)
