The Senate is expected to vote on the bill that would restrict abortion after 20 weeks on Monday afternoon.
The bill's sponsor, Representative Andy Mayberry, added an exception last week for rape and incest, which helped the bill clear the Senate committee.
If the bill passes this afternoon, ultimately the governor will have to decide whether or not to sign it.
House majority leader Bruce Westerman talked with reporters this morning about what he thinks Governor Beebe should do.
"Governor Beebe has expressed varying levels of opposition to these pieces of legislation, but he's never gone as far as threatening a veto," Westerman said. "I personally believe the governor would like to avoid vetoing legislation based on his prior service in the legislature."
Beebe has said he has serious constitutional concerns about this 20-week abortion bill, but hasn't said whether he will veto it.
Governor Beebe is at home with a cold today.