The politics of this seem highly dubious, but we can worry about that later. The interesting part is the "deeming" trick. Republicans have used it before, and it's been challenged and upheld in the Supreme Court. So there's little doubt that, even though any normal person would instantly recognize this as a shady, undemocratic, shyster trick, it's probably technically legal.
Former prosecutor Andy McCarthy tries to make the case that it's OK that the trick has been used by Republicans before, because those were for "uncontroversial" measures, like raising the debt ceiling. It still shouldn't be used, he says, for passing such a major piece of legislation as the health care bill.
Sure, we don't make lawmakers dot every "i" and cross every "t" every time. But that doesn't mean we've abandoned the right to make them play it by the book when it comes to a controversial matter. When there's a real dispute, they have to pass the bill the regular, constitutionally mandated way: Both houses on the exact same text, with every legislator accountable for his vote.
An alternate solution is simple and, I think, preferable: make lawmakers dot every "i" and cross every "t" every time. McCarthy's analogy to a criminal trial is false: such trials happen every day, incur significant expenses, and have a well-established appeals process if something goes wrong. Legislation in Congress, on the other hand, only passes a few hundred times a year at most (with only a few dozen bills a year that are controversial), has widespread consequences, and cannot be repealed without another act of Congress (or Constitutional invalidation).
Furthermore, as McCarthy says, "stipulation" happens in nearly every trial. The Slaughter procedure is invoked only rarely. And when it has been in the past (by Republicans), it was challenged by Democrats on Constitutional grounds, which leads me to believe that the legislation involved was not uncontroversial. (It's undeniably true that raising the debt ceiling is less consequential that the health care bill. But that was not McCarthy's argument: he said "controversial.")
The unfortunate but inescapable conclusion is that Republicans helped create this legislative environment by their own trickery, and now they are reaping the consequences. We all may end up paying dearly as a result.