Just Because It's Clever Doesn't Mean It's Consitutional

 Is the "Slaughter Solution" constitutional?  Here's the relevant text from the U.S. Constitution:

Article I, Section 1: All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives.

Article I, Section 5: Each House may determine the Rules of its Proceedings...

Article I, Section 7: Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a Law, be presented to the President of the United States; If he approve he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated, who shall enter the Objections at large on their Journal, and proceed to reconsider it. If after such Reconsideration two thirds of that House shall agree to pass the Bill, it shall be sent, together with the Objections, to the other House, by which it shall likewise be reconsidered, and if approved by two thirds of that House, it shall become a Law. But in all such Cases the Votes of both Houses shall be determined by Yeas and Nays, and the Names of the Persons voting for and against the Bill shall be entered on the Journal of each House respectively. If any Bill shall not be returned by the President within ten Days (Sundays excepted) after it shall have been presented to him, the Same shall be a Law, in like Manner as if he had signed it, unless the Congress by their Adjournment prevent its Return, in which Case it shall not be a Law.

Every Order, Resolution, or Vote to which the Concurrence of the Senate and House of Representatives may be necessary (except on a question of Adjournment) shall be presented to the President of the United States; and before the Same shall take Effect, shall be approved by him, or being disapproved by him, shall be repassed by two thirds of the Senate and House of Representatives, according to the Rules and Limitations prescribed in the Case of a Bill

For your information, the Slaughter Solution is the idea that the House can pass the Senate healthcare reform bill and its budget-related amendments under a single reconciliation vote.  In doing so, the House would only need a simple majority rather than two thirds to pass.

However, one needs to look no further than Article I, Section 7 to determine that the passing of one bill may not be also deemed the passing of another.

If you check out the Supreme Court opinion on Clinton v. City of New York (1998), each house of Congress must approve "precisely the same text."  Under the Slaughter Solution, the House would be approving a version different than the Senate.