Strategies of (unintended) precommitment

Geoff Robinson writes to me and speculates:

I was thinking that Scott Brown's election was instrumental in yesterday's passage of the health care bill, in the game theory sense.  The Senate managed to pass a bill, and then, with Brown's election, credibly declare that it would not be able to consider any changes to the bill. No health care legislation would make it through the body again. House Democrats, faced with this take it or leave it scenario, were forced to pass the Senate version without modification (or let it fail).

I wonder how things would have proceeded if Martha Coakley had won?  The House would have had (and certainly used) the option to force changes. This would have required the Senate to hold its super-majority coalition together for one more vote. Would all 60 senators have held the line? Would the use of reconciliation have been a viable political alternative? Would we have been debating health care all summer as negotiations dragged on?

My guess is the bill still would have passed, nonetheless this is an interesting exercise in the idea of unintended consequences.