There are some wranglings and restrictions on reconciliation that make this approach problematic. But I think this FoxNews piece is right about a lack of trust being a major roadblock. The House doesn't trust that the Senate will pass the reconciliation bill. But the House trusting the Senate isn't a roadblock at all.
From the FoxNews arcitle:
But what if the Senate never passes a second bill?
Now that's really the kicker. Because under the pitched scenario, no reconciliation to go along with the Senate bill would mean the President doesn't sign both. The House doesn't really need to trust the Senate. The House just needs to trust Obama not to stab them in the back if things get hairy in the Senate.
But let's be realistic. Suppose health care reform is sitting on the President's desk. There's no reconciliation package to go with it. Obama is a signature away from achieving his goal. He doesn't care what the > 50% of Americans who oppose this bill think. Do you really think he's concerned with double-crossing a couple hundred Representatives to get it done? And that is the main trust issue. The House doesn't trust the Senate but they don't have to. The House does have to trust the President. The lack of trust between the House and Obama is what is threatening this plan.