Such action already passed the house yesterday, and I’m sure it’s due to pass in the Senate.
I am grateful to Speaker Pelosi and House Democrats and Republicans for taking urgent action to prevent a rail shutdown. This overwhelming bipartisan vote in the House of Representatives makes clear that Democrats and Republicans agree that a rail shutdown would be devastating to our economy and...
The question really isn't whether the Senate will pass it or not. It will. The question is how fast they can do it. If they can pass it by unanimous consent, they can do it very quickly. However, if they cannot get unanimous consent, if even one Senator objects, it will take some days to go through required Senate procedural votes. Some industries will start halting vital shipments this weekend, and Amtrak will probably start cancelling trains on Tuesday absent certainty that a settlement will be in place.
Without the 7 day sick leave addition (which, in full disclosure, I personally support), which is a separate piece of legislation passed by the House, it appears likely that at least some Senators will not support unanimous consent. However, had the House included that in a single piece of legislation, that legislation certainly would not have had unanimous consent and likely would not have passed filibuster (that separate 7 day sick leave bill probably will not pass filibuster, btw). The list of Senators that may object to unanimous consent includes Senators diverse as both Sanders and Rubio. I am sure that both Schumer and McConnell are whipping for unanimous consent for the base settlement bill, as is President Biden, that statement you linked is largely intended as pressure on recalcitrant Senators on the Democratic side, but whether they'll get it is far from certain if not downright doubtful.
Politics is performative.
Congress will almost certainly force the settlement. Whether they do so in time to avoid all potential effects of the strike threat is another question. At least some shippers and probably Amtrak will prepare for one until that "almost" is removed.