First, I do not believe that Austin said that US troops might have to go to Ukraine, he said Europe. The implication is that an emboldened Putin would attack NATO countries next and our military would have to deploy. Which I suppose is possible, but highly unlikely IMHO. He's not in any position to start a war that would be far bigger than the one he's got now in Ukraine, so I don't see that happening.
It seems to me that if the European countries stop sending military aid to Ukraine then so should we, but as long as they're doing it then so should we. It might be that if we continue to support Ukraine that Putin will sue for peace or at least a cease-fire. Frankly, I'm not seeing the threat to our national security regardless of what happens there. And I think Putin is going to think long and hard about his next step in reconstituting the old USSR, considering how much difficulty he ran into in Ukraine.
The thing about tying the Ukraine aid with border security here, is just your basic American politics when one side doesn't have enough votes to do whatever they want to. Both sides do it when they are the minority party, and besides I don't see a problem with building a wall and improving security there. There is a national security issue there, moreso than the Ukraine, who knows who and what is being transported across our southern border. Not that the problem there would be resolved, but possibly reduced. hat ought to be a higher priority IMHO.