While Waxman said "it's something that could be passed this week," it remains to be seen whether the Senate would be receptive to the proposal.
Stakeholders have been tracking the discussions for months as key negotiators -- Davis, Waxman, Senate Homeland Security and Governmental Affairs Chairwoman Susan Collins, R-Maine, and Sen. Thomas Carper, D-Del. -- grappled with drafting a conference report.
According to Waxman, the proposal includes "a lot of accommodations for concerns were raised by" Collins and Carper, including a rate cap.
The overhaul bill that passed the Senate 99-0 in February would require the postal service to set rates according to inflation, a provision favored by mass mailers who want a bill that ensures the lowest possible prices.
The Davis-Waxman proposal offered Monday would uphold the Senate's version of the rate cap for 10 years, when the service would get access to a growing escrow account. Management of that account, which is another major sticking point, would be opened up in 2016 for the postal service to pay unfunded health retirement benefits.
The postal service is currently paying into an escrow account controlled by the Treasury Department.
A congressional aide close to the negotiations admitted that the House and Senate remain "deadlocked over literally dozens of issues," but said the Davis-Waxman offering had the best chance of pleasing all sides of the mailing community.
The National Association of Letter Carriers has criticized a proposal by Collins, which included a provision to require postal workers to wait three days before being eligible for worker compensation benefits.