"Kind of civics class by crisis."

And one should be cogent of the maxim that "Hard cases make bad law." That from the judicial side of things, but apropos here.

On the other hand, I think we're fortunate to have a meta-process that the public is involved in, that seems to work better than a lot of the alternatives.

As for your question and uncertainty, I've seen quite a bit of good discussion at The Volokh Conspiracy in the comments to various postings (http://volokh.com/, it's a high quality group law blog by various law professors and the like). (In fact, if you haven't visited it before, check it out, all sorts of tasty stuff right now, e.g. the 11th Circuit has just made what is possibly a bad ruling on email and 4th Amendment search and seizure. I wish I had time to follow it...).

In the discussions you'll find some comments on at least one prior ruling by the Supremes in this area; they are very reluctant but not entirely so.

While the House has very broad discretion to make its own rules, the Supreme Court case striking down the line item veto provides pretty strong authority for saying that a "deemed enacted" method of purporting to pass a bill would violate Article 1, Section 7 of the Constitution.

According to Article I, Section 7, in order for a "Bill" to "become a Law," it "shall have passed the House of Representatives and the Senate" and be "presented to the President of the United States" for signature or veto. Unless a bill actually has "passed" both Houses, it cannot be presented to the president and cannot become a law.

In striking down the line item veto, the Court (in the case of Clinton v. City of New York (1998)) rested its decision squarely on the requirements of Article 1, Section 7, stating as follows:

"[O]ur decision rests on the narrow ground that the procedures authorized by the Line Item Veto Act are not authorized by the Constitution. The Balanced Budget Act of 1997 is a 500-page document that became 'Public Law 105-33' after three procedural steps were taken: (1) a bill containing its exact text was approved by a majority of the Members of the House of Representatives; (2) the Senate approved precisely the same text; and (3) that text was signed into law by the President. The Constitution explicitly requires that each of those three steps be taken before a bill may 'become a law.' Art. I, sec. 7. If one paragraph of that text had been omitted at any one of those three stages, Public Law 105-33 would not have been validly enacted. If the Line Item Veto Act were valid, it would authorize the President to create a different law, one whose text was not voted on by either House of Congress or presented to the President for signature. Something that might be known as 'Public Law 105-33 as modified by the President' may or may not be desirable, but it is surely not a document that may 'become a law' pursuant to the procedures designed by the Framers of Article I, sec. 7, of the Constitution."

Michael McConnell, a Stanford constitutional law scholar, explained the problem with the Slaughter rule ("deemed enacted") as it would apply to this case:

"The Slaughter solution attempts to allow the House to pass the Senate bill, plus a bill amending it, with a single vote. The senators would then vote only on the amendatory bill. But this means that no single bill will have passed both houses in the same form."

Ergo, a clear violation of Article 1, section 7, as recently interpreted by the U.S. Supreme Court. This is not so much a political issue as a legal one - if this rather desperate approach is used to attempt to pass this bill, it will very likely be struck down as unconstitutional, notwithstanding the House's otherwise broad discretion in regulating its own affairs.