House Speaker John Boehner (R-Ohio) called on all House members to support a resolution naming a room in the Capitol Visitor Center after the slain aide of Rep. Gabrielle Giffords' (D-Ariz.).
Gabe Zimmerman became the first congressional staffer to be killed in the line of duty.
But that plan was abandoned in favor of Wasserman Schultz's measure. Boehner took to the floor Wednesday to urge its passage.
"An attack on one who serves is an attack on all who serve," he said. "I don't think I fully understood the meaning of those words until last January's senseless assault on our fellow citizens and our most fundamental responsibilities.
"This House responded in prayer and solidarity, reminding the world that no act of violence could silence the sacred dialogue of democracy.
"It is in that same spirit that later today we will gather here to honor Gabe Zimmerman, the first congressional staffer to give his life in the line of duty, and, God willing, the last," Boehner continued. "Like every member of this body, he took an oath to uphold and defend our Constitution, and he died while well and faithfully discharging his duties, and I think it is fitting and appropriate to honor Gabe Zimmerman with a permanent memorial in the United States Capitol.
"I extend the thanks of the whole House to Gabe's family for their participation in this project. Let us honor Gabe's memory by following his example of service to this institution, which remains the direct voice of the American people and their will.
"So later day, I would ask the House to support the resolution," he concluded.
The House will debate on Zimmerman resolution Wednesday. The vote will take place on Thursday.
Wasserman Schultz, a close friend of Giffords, led the way on the measure, which will name HVC 215 of the Capitol Visitor Center the Gabriel Zimmerman Meeting Room. The community outreach director for Giffords was one of six people killed in the Jan. 8 shooting in Tucson, Ariz.
The resolution had languished in committee while Boehner took over efforts to honor Zimmerman. But last week Wasserman Schultz's measure appeared on the House calendar for this week, and the Speaker's office said it was supporting her legislation.
-- This story was last updated at 2:23 p.m.