It's an 80-day cooling period, so you are talking Dec 20th if it happened right now. It will take at least 3-5 business days to go through the steps to use Taft-Hartley though, which gets you to Christmas. The problem is that if you go to Taft-Hartley now, you will (further?) alienate the Teamsters, ULAW, and ILA. That would even potentially trickle down to other unions, which would be a political disaster in the Rust Belt states. Unfortunately, these are all moves that are only being viewed through the lens as a political item, knowing full well that they will have repercussions well past the election.
The blame is, to some extent, on all parties involved at this point. The problem is that for the good of the country the "bad guy" in this scenario should have been the federal government. Unfortunately, instead of taking the hit and making it known well in advance that they would force a resolution through Taft-Hartley, the signals were instead that the government wasn't going to get involved. Now, the ILA knows that they can strike up until Nov 6th as leverage. Also this means the USMX knows what the expected maximum of how long they have to hold out until they could possibly see government intervention. So if you are USMX you start to do the math and figure out what the cost of 35 days of strikes will be to you and how much is that going to impact you long-term.
So if you are the ports are you willing to move above your current offer, which moved right before the strike from 30% to a 50% raise over 6 years? If you are the ILA do you move off your position knowing that the 50% is now the floor the NRLB would consider as the negotiated settlement?
The timing makes this such that there isn't a ton of reasons for either side to be willing to move off of their position. The whole situation is a misstep all the way around.