Postal workers around the country on Tuesday held demonstrations near the offices of all House members, urging them to support legislation that would allow the U.S. Postal Service (USPS) to reschedule future retirement payments that are threatening to shut down the service completely.

Various local news outlets reported the demonstrations, including those at key Republican offices. Three of these took place at the offices of the three House Republican members of the deficit reduction supercommittee — House Republican Conference Chairman Jeb Hensarling (Texas), House Ways and Means Committee Chairman Dave Camp (R-Mich.) and House Energy and Commerce Committee Chairman Fred Upton (R-Mich.).

The National Association of Letter Carriers (NALC) said rallies were scheduled at all local House offices. Reports noted rallies at the local office of House Majority Leader Eric CantorEric CantorTrump nominates two new DOD officials Brat: New ObamaCare repeal bill has 'significant' changes Overnight Energy: Flint lawmaker pushes EPA for new lead rule MORE (R-Va.) and several other House Republican offices, as well as the office of Rep. James Clyburn (S.C.).

Clyburn and scores of Democrats support, H.R. 1351, which the NALC asked members to support. That bill, from Rep. Stephen Lynch (D-Mass.), would end a 2006 requirement that the USPS pre-fund decades of planned retiree benefits. It also has a few dozen Republican sponsors.

Still, other Republicans seem to be considering solutions to the USPS fiscal woes that involve significant cost-cutting at the USPS, rather than ways to let the service simply reschedule or rearrange its retiree benefits.

House Oversight and Government Reform Committee Chairman Darrell Issa (R-Calif.) and Sen. John McCainJohn McCainEx-Bush aide Nicolle Wallace to host MSNBC show Meghan McCain: Obama 'a dirty capitalist like the rest of us' Top commander: Don't bet on China reining in North Korea MORE (R-Ariz.) have introduced legislation that would create a panel that would recommend cost-cutting measures at USPS, including office closures.

-- This story was updated at 3:00 p.m. to clarify that postal service rallies were held at all House member offices, and other details.