The House must pass the Senate bill first. The Senate cannot reconcile with no exact bill in the other chamber.
There is even question as to whether BO has to sign the Senate bill into law (assuming the House votes for the Senate bill as is) b4 they take up any reconciliation measure.
You make an interesting point.
It does seem possible that the Senate could take up a Reconciliation Bill before Obama signs the original bill into law. But they couldn't pass it until he does. Given that this is the case it opens up the possibility that Obama could promise to veto the Senate bill if there is no subsequent Reconciliation Bill passed by the House and the Senate. That would be done as an inducement to get the House to pass the original Senate Bill.
Would Obama do that? Would the affected Congressman trust him? Would the Republicans stall the reconciliation process indefinitely? What would the voters think of this spectacle? This is almost as good as Edgar Allan Poe and Sherlock Holmes. Where's the popcorn maker?