This is the key...

On the surface, "Deem and Pass" (AKA "The Slaughter Rule" -- named after the Chairwoman of the House Rules Committee)---the method the democrats are proposing to pass the health care bill---might be unconstituional, but I'm no lawyer. That said, I can read and the Constituion appears to be pretty cut-and-dry that "[v]otes of both Houses shall be determined by Yeas and Nays"...

Article I, Section 7 of the U.S. Constitution states: "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.”

Put simply,

"...instead of House members casting their votes on the Senate version of the health-care bill, the House would vote on a package of “fixes” made to those parts of the Senate bill to which House members object...Under the House’s “self-executing rule” provision, if the lawmakers pass a rule that says passing the “fixes” is the same as passing the actual bill -- then the House would magically "deem" the health-care bill to be “passed.” The "rule" itself would be sponsored by the chairman of the House Rules Committtee, Rep. Louise Slaughter (D-N.Y.)."

Source: http://www.cnsnews.com/news/article/62939