Tax reform "has a proven record of creating jobs," Wyden said Tuesday. But Wyden and Coats may be out of luck. Boehner on Saturday abandoned talk of a debt deal that would have included tax reform.
Republicans have also gotten into the act. Freshman Sen. Pat Toomey (Pa.) released his own budget in May that would balance the budget by fiscal 2020 by dramatically reducing spending and turning Medicaid into a block-grant program.
Other Senate GOP freshmen have gravitated toward the issue of the deficit as a way of burnishing their conservative bona fides. Sen. Ron Johnson (Wis.) launched a short-lived filibuster last month that slowed business on the Senate floor in order to force Congress to debate the deficit matter.
Another recent arena where lawmakers have sought to influence the debate is the Senate floor, where the chamber is considering a nonbinding measure — sponsored by Democrats — that expresses the Sense of the Senate that millionaires should share in any "sacrifice" required to reduce the deficit.
Among the amendments that have been filed to the measure is a proposal from Sen. John McCain (R-Ariz.) that would allow taxpayers to designate their taxes for deficit reduction, as well as a separate amendment that would allow for fast-track procedures for spending rescissions.
Sen. Dean Heller (R-Nev.) wants to offer an amendment that would prevent Congress from being paid until there is a budget deal.
Still, some lawmakers say it's more realistic to believe that the White House negotiations will be unaffected by the plans that have been offered.
Sen. Bob Corker (R-Tenn.) said many of the plans that have been floated are for "messaging" and designed for "public consumption."
"We would be much better off in this body if we did things under regular order," Corker said. "All these things that happen in private give the ability, candidly, for both sides to message."