Democratic Rep. Sander Levin [said] "We're going to be amending the law"...This is different from the problem discussed in the Michael McConnell post. McConnell's argument was based on the necessity of seeing the 2 bills as one. This new problem arises when you assume there are 2 bills. If a separate bill is just a package of amendments, and if it must be aimed at "current law," then you can't merge the vote, because even if the Senate bill is "deemed" passed, putting it first in time before the passing of the package of amendments, there's no procedural trickery that can get the President's signature into that time sequence. Even if you can fiddle with time somewhat, you can't do that.
[Democratic Rep. Henry] Waxman added, "We change current law, and the current law will be the Senate bill once it's voted on in the House."
But it won't be law until the president signs it.
UPDATE: "Democratic lawmakers and an aide to House Speaker Nancy Pelosi, D-Calif., say they've dropped plans for an indirect vote that would have relied on a legislative maneuver to give their OK to the Senate's version of health care legislation." Good. So, now, once it is undeniable that the House is passing the Senate bill, will the votes be there?