That’s the plan. The House approves the Senate version and voila, it’s just 51 Senate Votes for Rainbows and Unicorns.
If the house approves the Senate bill (which many house members do not like) as is, then the bill is ready for presidential signature. What is to stop Obama from signing the Senate bill as is? Now as I understand it the house will be trusting the Senate to make the bill look like what the president?? or house wants. But I guess Pelosi can hold the approved Senate/House bill away from Presidential signature until next year or passage of A Senate reconciliation bill to her liking.
If the Seate cannot do reconciliation then Obama might have to Veto the Senate Bill. The Senate bill is unworkable as is.
The House won't approve the Senate version, if they did, they weren't even need a revote in the Senate.