Senate Majority Leader Mitch McConnell (R-Ky.) at the U.S. Capitol on July 25. (Win McNamee/Getty Images)

Senate Majority Leader Mitch McConnell (R-Ky.) plans to bring a bill to undo the Affordable Care Act to the Senate floor next week, a McConnell spokesman said Wednesday.

His statement marked McConnell’s most concrete commitment yet to moving ahead with the bill from Sens. Bill Cassidy (R-La.) and Lindsey O. Graham (R-S.C.). It signaled that a vote would be expected next week.

“It is the Leader’s intention to consider Graham-Cassidy on the floor next week,” said McConnell spokesman Don Stewart.

The announcement came as Republican leaders and the White House were trying to rally support for the measure. Cassidy and Graham met Wednesday with Alaska Republican Sens. Lisa Murkowski and Dan Sullivan, who have not yet said whether they support the plan.

The bill would convert funding for the ACA into block grants for the states and would cut Medicaid dramatically over time.

McConnell has until Sept. 30 to hold a vote on the bill under special procedural rules that would allow it to pass with just 51 votes instead of 60. Republicans would need 50 out of 52 Republican senators to support the legislation, with Vice President Pence standing ready to break a tie. No Democrats are expected to back it.

It is not clear whether McConnell can get 50 votes. Already, Sen. Rand Paul (R-Ky.) has come out against the bill. Other key senators have signaled concerns. Some Republicans have said they think McConnell will not hold a final vote unless he has the numbers to pass it.

Asked whether the Wednesday announcement meant that a vote was guaranteed, Stewart simply repeated his earlier comment.