Per Chait's suggestion about doctoring the stimulus bill in the conference committee, it seems like the obvious fix here is ditching the AMT measure, which costs just under $70 billion, and adding back in the state aid and school construction money (about $56 billion). That would make the Senate bill look a lot more like the House bill, basically ensuring passage in the lower chamber. And the senators who were most adamant about the AMT patch--namely, Chuck Grassley--don't look like they're voting for the stimulus anyway, so no real loss there.
On top of which, the AMT measure is about as far from resembling stimulus as anything in the bill--it's cash for upper middle-class people. As Tom Edsall points out in this helpful piece, the bang for your buck from the AMT fix is likely to be about one fifth the bang for your buck on state aid. I'd love to know what economic theory Susan Collins, Ben Nelson, and Arlen Specter used to justify keeping the former and ditching the latter. I'm sure it's a good one.