Andrew is right only if the Democrats start thinking like him. There are perfectly viable ways to pass a major health care reform without taking another vote in the Senate. The easiest is just to have the House pass the Senate bill, and promise to use a reconciliation bill, which requires just a majority vote, to smooth out any changes. It's very, very doable. It's also in the interest of the Democrats in Congress. They already cast a vote, might as well reap the benefit of having an accomplishment.
The only question is whether they can keep their heads.