You are most likely correct but what the heck, if there ever was a time to dig in their heels, it is now for the house republicans. If domestic border security is at least as important as Ukraine, then they go together, and if there can be only one, then let it be border security.

There's a difference between digging in your heels and making it very clear that no deal is possible. And that anyone who tries to negotiate a deal will be blasted politically. There's no doubt that if the House GOP is only offering HR 2 and nothing, there will be no border bill. And now that the Senate knows that there will be no border bill, they're not going to bother negotiating a border bill.

So you end up with the exact opposite of the situation you hope for above. The border bill is dead, and if there can be only one, it will only be Ukraine funding. The likelihood is that no bills pass, of course - but the next most likely outcome is a clean foreign aid bill, and the possibility of a border bill the least likely of all.