Per a source familiar with the White House conversations:
I also asked a senior congressional source — someone who's been very skeptical about Zombie Trumpcare's prospects — whether it's possible there's a vote this week before Congress goes on recess. The source's response this morning was the most hopeful I've heard from them: "I think it's possible. If we feel like there is momentum we'll keep the members here until it's done."
Bottom line: Conservatives remain wary that the White House will "go back on its word" and they're going to carefully scrutinize the text when it finally arrives. And House moderates are more than wary of the Freedom Caucus — many simply hate them and believe they are dishonest and incapable of getting to "yes."