Bipartisanship is tough. If you think the GOP just happened upon the idea of obstructionism in 2009, think again. The 1993 healthcare bill was specifically targeted for failure by the GOP, not because of specific policy disagreements, but because they knew that successful healthcare legislation under a Democratic president would be a PR windfall, and an electoral disaster for the GOP.
So just like previous threads on the board where we talk about stopping obstructionism in 2009, we have to find a way to stop it in 1993. I understand how partisan it is to say this, but the easiest way is probably to get the Dems to 60 in the Senate. Lotta close races in '92. A nationwide swing of about 1.5% would see five more seats go to the Dems and put them up to 61.
The state of partisanship today, the GOP still wouldn't come to the table if you invited them, but in the early 90s things are just heating up, and I have to imagine the party would welcome the opportunity to make the bill more conservative in exchange for a show of bipartisanship. Or at least the remaining moderate faction would.