Timothy. You claimed that the House originated President Obama's budget proposal. Citation needed please.
It does. The executive proposes the budget as required by the Budget and Accounting Act of 1921. The House turns the proposal into a bill, as required by the Constitution, editing it as it sees fit along the way. The executive can not create a bill. The bill then follows the normal constitutional procedure for introduction into the Senate, passage in both houses, reconciliation of the versions, and submittal to the executive for signature or veto.
The Constitutional requirements are actually very simple. Here they are, verbatim (including the habit of arbitrary capitalization of nouns common at the time):
"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." —US Constitution Article I, section 7, clause 1.
"No money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of Receipts and Expenditures of all public Money shall be published from time to time." —U.S. Constitution Article I, section 9, clause 7.