The Congressional Budget Office released their scorecard on this bill and it can very likely spell big trouble for its proponents. They predicted that 24 million Americans would lose their access to affordable health insurance in the next decade, 18 million of them in 2018 alone, if the bill were passed into law.
I'd be shocked if Senate Republicans allow this to sail through after this report. The House may very well send it to them, but more than enough Republican Senators have expressed deep concerns about the bill that would make it nearly impossible to get through the upper chamber.
Anything can happen, but I have a feeling the Senate is going to put the breaks on this and try to come up with their own bill that would get a better CBO score. The question then becomes if the House Republicans would be able to cobble together enough votes in their chamber to pass whatever the Senate sends them. And that's a big task concerning the various factions within the House GOP Caucus.