A key House Republican lawmaker expects a vote during the first week in May on a new version of a health bill to be negotiated between Congress and the White House, even though the measure would not amount to a repeal of Obamacare.

“i think the odds of that are pretty good,” Representative Dave Brat of Virginia, a member of the far-right House Freedom Caucus, said in a radio interview Friday with a Richmond radio station.

Brat said that if compromises that conservatives and moderates have worked out with the administration materialize when the bill is written, “that gets a lot of us toward a ‘yes,’ along with a couple of other items we’ve been negotiating.”

House Republican leaders and the White House haven’t announced a target date for a vote. But Speaker Paul Ryan said on April 19 that lawmakers were already negotiating “finishing touches.”