The legislation would stop either party from using Presidential Election Campaign Funds for party conventions beginning in 2013, The Hill reported Monday.
"Voluntarily returning convention funds would be a great act of leadership and statesmanship for both parties," Coburn said Monday in a statement. "Nevertheless, it's time for Congress to act and end the practice of subsidizing annual convention parties with taxpayer dollars."
Through Presidential Election Campaign Funds, the parties each receive $18.3 million for their nominating conventions.
Udall said American taxpayers shouldn't have to pay for nominating conventions that have become more partisan during the last few decades.
"Over the past several decades, political party nominating conventions have become elaborate celebrations devoted to partisanship," Udall said in a statement Monday. "The American taxpayer should not be responsible for footing the bill for these partisan events."
The Republican National Convention is Aug. 27-30 in Tampa, Fla. The Democratic National Convention is Sept. 3-6 in Charlotte, N.C.