Yeah, that’s not caving, that’s DARING Congress to refuse to pass the bill.
See, they were going to pass a budget bill that has some border funding in it, and Mitch McConnell was telling the Republicans to pass the darned thing – but then Trump said it might be nice to use the border mess in his campaign, and Poof! McConnell spun around so fast, his heels were smoking! (no, not literally) Here’s a link: https://news.yahoo.com/trump-thrown-wrench-mitch-mcconnell-214452142.html
The statement from Biden is a double-dog dare to not pass the bill. Every time Republicans cry, “Waaahh! Border scary! Biden’s fault!”, Biden is going to hold up that statement and point out that he was ready, but they refused to sign it.
He’ll say it, but only newsy Democrats will hear him. The Republicans will say the bill didn’t go far enough, cost too much, and blah, blah, blah, glossing over the crazy powers it would have allowed. This isn’t any special ‘5d chess’, this is standard politics. Biden knows Congress won’t do ANY border deal now that Trump told them not to, so it doesn’t matter what concessions it has.