The House and the Senate have been acting under the assumption that only if both houses pass the same bill can a reconciliation “sidecar” be introduced. If the House passes the Senate bill, they would have to trust Obama not to sign it into law until the Senate has passed the sidecar.
And don’t bills passed through budget reconciliation have a ten-year sunset for public spending?
Legislative rules are pretty fungible. The question is how much they want to bend or break the precedent to achieve their goal. Or rather, how badly they want health care.