Speaker John Boehner drew a firm line on taxes tonight, saying that Republicans’ retention of the House majority is a sign the public does not want a tax rate hike.

With CNN and NBC projecting that the GOP will retain the House majority, Boehner and National Republican Congressional Committee Chairman Pete Sessions (Texas) took the stage at the GOP’s victory party in Washington, D.C., to cheer on the crowd.

“The American people want solutions, and tonight, they’ve responded by renewing our majority,” the Ohio Republican said. “With this vote, the American people have also made clear that there is no mandate for raising tax rates.”

Republican National Committee Chairman Reince Priebus did not join them onstage, although the official schedule released earlier in the day had listed him as speaking before Sessions.

With Democrats claiming several Tossup Senate seats, the path to victory for Republicans in that chamber is slimming. The presidential contest remains extremely close as well.

Boehner thanked Priebus from the stage nonetheless. He also thanked GOP presidential nominee Mitt Romney and vice presidential nominee Rep. Paul Ryan (Wis.), who, he said “carried the banner of our party with grace, vision, strength and dignity.”

“We stand ready to work with any willing partner — Republican, Democrat or otherwise — who shares a commitment to getting these things done,” he said. “We’re humbled to have again been entrusted by the American people with the responsibility of leading the People’s House. We’ll never take it for granted, and we won’t let you down.”

Sessions, who introduced Boehner, called the House an “incubator of ideas.”

“We will continue to work with the American people on ideas that will make our country stronger, more competitive and will build back the American dream,” he said.