House Democrats and Republicans want more control over the appointment of the Architect of the Capitol, but it’s unclear whether the Senate will go along with their plan.

Currently, a commission of Congressional leaders recommends three candidates for the position, and the president makes the final choice, subject to Senate confirmation. But, a group of House Members argued, it’s a slow and often frustrating process that can lead to an unreasonably long vacancy: Former Architect Alan Hantman ended his tenure more than a year ago, and Members say the process for replacing him has completely stalled.

On Wednesday, Reps. Debbie Wasserman Schultz (D-Fla.) and Zach Wamp (R-Tenn.) announced a bill that would hand the entire appointment process over to Congress. Under the bill, a group of House and Senate leaders would preside over the selection of an Architect.

As the process exists now, it’s a “huge, huge job with a lot of masters,” said Wasserman Schultz, who oversees the AOC’s budget as chairwoman of the Appropriations Subcommittee on the Legislative Branch.

“This bill takes the responsibility of the appointment of the Architect and puts it where it rightfully belongs,” she said. “This is a long-overdue change.”

Rep. Ray LaHood (R-Ill.) called the current process “archaic,” while Rep. Tom Latham (R-Iowa) said it is “a broken system.” Congress oversees the Architect’s actions, they said, and yet Members can’t control who gets the position. And the long tenure — 10 years — means Congress is stuck for several cycles with whomever the White House chooses.

But the Senate’s view was less enthusiastic Wednesday. Under the current system, Senators hold more power than the House in appointing the Architect because they confirm the eventual nominee. The proposed process would shift some of that power to the House.

“When this issue has been raised before there were serious concerns about diminishing the advice and consent authority of the United States Senate,” said Howard Gantman, spokesman for Senate Rules and Administration Chairwoman Dianne Feinstein (D-Calif.).

Stephen Ayers is now the acting Architect of the Capitol, and he has overseen the tail end of the AOC’s biggest project, the Capitol Visitor Center. The CVC will open on Dec. 2 — perhaps without a permanent Architect in place.