A major housing affordability bill poised to clear the Senate as soon as Thursday will hit a wall in the House, in part over concerns about a ban on major investors from buying single-family homes.

During a meeting at the House Republican retreat this week attended by the party’s leaders and committee chairs, Majority Leader Steve Scalise, R-La., predicted the housing measure is likely to bog down due to differences between the House and Senate versions. He said that if the Senate doesn’t address wide-ranging concerns from House members and House Financial Services Chair French Hill, R-Ark., the bill is likely to require discussions between the House and Senate before it could become law.

“If the Senate thinks we’re gonna take this medicine, we’re gonna go to conference” committee, Scalise said, according to three attendees, who asked not to be named because they were speaking about a closed-door meeting. A conference committee is made up of lawmakers from both chambers who are charged with reconciling differences between legislation that’s been approved by the House and Senate.

The housing package has received a rare degree of bipartisan support in a bitterly divided Congress. A House version of the bill passed 390-9 in February, while the Senate measure has advanced through procedural votes with more than 80 votes supporting it.