They do, and this will, by virtue of procedure, from the article:
The Senate plans to attach Obamacare to a House-passed non-healthcare bill.
This has been done any number of times over the course of our history, the Senate strikes the language of a House bill and inserts its own text, it requires the bill going back to the House to get the 218 for passage. But as I just wrote, this is not a guarantee, especially if the Senate does not include the Hyde language re: no federal funding for abortion but the exceptions, if this is not in the Senate bill, Stupak has promised Pelosi that he does have the votes and will kill the bill. I do not know at this point if any member of the Senate offered the amendment, as the language was not included in the Baucus deal presented.
Then it originated in the Senate. I see your point, but if only the number is the same, or if the same tax and spend portions were not in the house bill, this method would seem to severely violate the intent of the constitution.