I don't think Trump cares about whether or not Obamacare is actually repealed. I'm nearly certain there was a reported conversation where he was asking Schumer if he could call an ACA stabilization bill "repeal and replace" and Schumer told him he could call it whatever he wanted.
He just wants a bill, any bill. Before the bill will be Obamacare, and after the bill something will have changed, ergo it is no longer Obamacare, ergo Obamacare has been repealed and replaced because we don't have Obamacare anymore. That's the sum total of his thought process on this. If he could sign a bill that did nothing but change the title of the current law to "Trumpcare," he would, because his only policy objective here is to one-up Obama.