Democrats can be expected to oppose the deeming resolution, but Republicans noted that similar resolutions have passed in years where there is no agreed-upon budget resolution, and this time blamed the Senate for failing to pass a budget for the last three years.
Once the rule is approved, that will start debate on the underlying gun-rights bill, the Sportsmen's Heritage Act, and several amendments. The bill eases rules on the use of firearms on federal lands, and also allows polar bear trophies to be imported into the United States.
Also Tuesday, the House will hold two postponed votes on non-controversial bills honoring Lena Horne and Mark Twain.
The Senate returns at 10 a.m., and at 11 a.m. will take another crack at moving ahead with a Democratic bill to reform the U.S. Postal Service (USPS).
The 21st Century Postal Service Act, S. 1789, would allow the USPS to restructure its retirement plan for employees, which many agree is now close to bankrupting the service, and give the USPS access to overpayments it made to its employee retirement plan as part of a plan to get back in the black.
The Senate tried in late March to move to the postal bill, but failed when Republicans insisted that the Senate continue debating a bill to raises taxes on oil companies.