Eric Cantor Tries To Make Laws Without Senate, President

I recall back to my earliest government classes when I learned the process a bill undergoes to become law, which requires a bill to pass through both chambers of Congress - the House of Representatives and the Senate - and then to the president's desk.  Sounds simple, right?

This is what the Constitution has to say about that (Article I, Section 7):

All Bills for raising Revenue shall originate in the House of Representatives; but the Senate may propose or concur with Amendments as on other Bills.

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.

Apparently Republican House Majority Leader Eric Cantor believes otherwise - in a new budget bill proposed by the representative, Cantor insists that if the Senate cannot decide on a budget by next Wednesday, the GOP's budget will become law.  To be exact, the bill states that "if the Senate fails to pass a measure before April 6, 2011 providing for the appropriations of the departments and agencies of the Government for the remainder of fiscal year 2011, H.R. 1 (as passed by the House on February 19, 2011) becomes law."

Does Cantor honestly believe the House can unilaterally pass legislation by simply saying so in the bill?  Does Cantor believe he can rule the country, ignoring the Democrat-controlled Senate and White House?

I wonder if this was taught in one of those constitutional classes Michele Bachmann held months ago...