Boehner said he had a proposal on the table that the President could have accepted last Sunday. That might be true. The President might have accepted it, but it wouldn't have been ratified by the Republicans in the House. Maybe what Boehner means is that with a few Democratic votes, he might have been able to get it passed without the amendment. However you gotta wonder if the Tea Party Repubs would have stayed on board if there were Democrats voting for it.
Ultimately, if there's going to be a bill that passes the House without the balanced budget amendment, it's going to require both Boehner and the President to support it. A fair number of Republicans will jump ship. And it seems pretty likely that Boehner will lose his speakership. There will be a lot of pissed off Republicans in the House (and elsewhere) if that happens.
The reporters have got something wrong when they say Boehner's bill would have them revisit the debt ceiling in January. With an overhang like that, it would never go away between now and then. The brinksmanship would continue unabated.
Also when they recite the song about the bond rating and the effect that might have on interest rates, I am doubtful. The world still needs a place to store value safely. Even after this lunacy the US will still be the safest place to store value. I've been asking people this question, where would you put money to find safety assuming the US credit rating was reduced. There is no other country to switch to. The whole downgrade thing is fiction, reported by people who don't understand it.
I think you're seeing all these machinations because the Tea Party caucus gets their power from the unwillingness of the old guard in the Republican Party to let them run the show. Imagine what would happen if Boehner stepped aside and let Michele Bachmann be the new Speaker. Or Ron Paul. You'd probably find the remaining Republicans (not a majority of the House, but a majority of the Republicans in the House) voting with the Democrats more often than they would vote with the Tea Party Republicans.