Sorry, no. No bill that imposed any tax originated in the House that subsequently became ObamaCare. The Senate adding such a tax later does not satisfy the Constitutional requirement, unless the funds collected by the tax are allocated by the law to a particular purpose or program. Such is not the case with respect to the mandate penalty, because Congress didn’t think it was a tax.
You are just wrong about this.
The bill the Senate passed started life as H.R. 3590 and was first introduced in the House.
That bill was then amended to insert ObamaCare.
You may not like the way that was done, but them's the facts.