Health Care Law would be a valid tax bill

I was asked an interesting question today that I honestly had to do some research on to verify or deny... I was asked if the mandate in the Health Care Law is a tax as it was defined by the Supreme Court, wouldn't the bill be invalidated then because it originated in the Senate and according to the Constitution, all tax bills MUST originate in the House of Representatives (as stated in Article I, Section 7.1)?

After a bit of research, I discovered that the answer is (sadly) no.  The bill actually DID originate in the House of Representatives in 2009 as HR  3590, Patient Protection and Affordable Care Act.  That bill was passed by the House Ways and Means Committee and then was passed by the full House.  The measure then went to the Senate where the Senate largely ignored it and instead focused on their own bill and passed that as an amendment to the House bill.  What then went to the Conference Committee to iron out was the House Bill that had been replaced in its entirety by a Senate amendment.  Within the rules and procedures laid out by the Constitution, this DOES qualify as a revenue bill that originated in the House of Representatives.

Doing this research has honestly made me wonder if the House and Senate Democrats knew all along that this mandate was a tax and therefore made sure it was the House bill that went to conference so that it was indeed a valid tax.  The adamant statements during the debate that the mandate was NOT a tax now bring to mind a paraphrase of the line from Hamlet, "The Democrats doth protest too much, methinks."