COLUMBIA, S.C. — The push to remove the Confederate flag from the grounds of the South Carolina Statehouse is about to clear its first hurdle.

But even if a bill to bring down the rebel banner passes the state Senate as expected Tuesday, it faces a less certain future in the House.

Senators voted 37-3 on Monday to take down the flag and the pole it flies on, both of which were erected in 2000 as part of a compromise that involved removing the flag from atop the Statehouse dome. The vote was well over the two-thirds majority that will be needed Tuesday to send the bill on to the House.

But while that means debate would begin Wednesday in the House, it is far from clear whether a vote will take place the same day — or what the vote will be. House members appear to be less unified.

Republicans met behind closed doors Monday and struggled to reach a consensus on what to do next. Some, including Speaker Jay Lucas, have not said how they will vote.

One idea being floated is to keep the pole and put a different flag on it: the U.S. flag, the South Carolina flag or a flag that may have been flown by Confederate troops but is not as divisive as the red banner with the blue cross and white stars.

Democrats, meanwhile, say both the flag and flagpole must go, House Minority Leader Todd Rutherford said.

Business leaders and Gov. Nikki Haley agree. If the bill passes and Haley signs it, the flag would be lowered for the last time and shipped off to the state’s Confederate Relic Room, not far from where the last Confederate flag to fly over the Statehouse dome is stored.

“The South Carolina Senate today rose to this historic occasion, with a large majority of members from both parties coming together in the spirit of unity and healing that is binding our state back together and moving us forward in the right direction,” Haley said in a statement.

Monday’s vote came at the end of a day of debate in which several white senators said they had come to understand why their black colleagues felt the flag no longer represented the valor of Southern soldiers but the racism that led the South to separate from the United States more than 150 years ago.

As the senators spoke, the desk of their slain colleague, state senator and the Rev. Clementa Pinckney, was still draped in black cloth. Pinckney and eight other black people were fatally shot June 17 during Bible study at a historic African-American church in Charleston. Authorities have charged a man who posed for pictures with the rebel banner. Police say he was driven by racial hatred.