Sen. Joe Lieberman, a longtime supporter of D.C. issues, is said to be searching for a way to help move a measure to give the District budget autonomy.
Any of these bills could theoretically contain D.C. budget autonomy language, but Issa says it's unlikely.
"Putting it with the tax extenders would be even harder," he said.
Some local activists haven't given up hope. A small contingent from DC Vote gathered outside the Longworth House Office Building on Wednesday afternoon, holding signs asking Congress to "Free D.C.'s Budget."
DC Vote Public Affairs Director Eugene Kinlow acknowledged that the "options are limited," but he said the organization is still exploring "creative options" to pass budget autonomy language before the end of the year.
Sen. Joe Lieberman (I-Conn)., the retiring chairman of the Homeland Security and Governmental Affairs Committee who has championed D.C. issues during his career in Congress, is also "search[ing] for avenues to advance the city's fiscal independence," according to his spokeswoman, Leslie Phillips.
Del. Eleanor Holmes Norton (D-D.C.) cited the leadership of Lieberman and Issa as a reason to feel hopeful for the future of D.C. budget autonomy.
Though she disputed the idea that the window is narrowing in the 112th Congress, she emphasized that the momentum that has grown around the issue will only help the cause going into the 113th Congress.
"We have made progress we couldn't have dreamed of a year ago," Norton said, adding that House and Senate leaders have begun to support a whole host of issues essential for the District's autonomy, such as language in appropriations bills that would allow the local government to spend its own funds in the event of a government shutdown.
Rep. Elijah Cummings, D-Md., right, hugs Harold Schaitberger, General President of the International Association of Fire Fighters, after the Congressman spoke at the IAFF's Legislative Conference General Session at the Hyatt Regency on Capitol Hill, March 9, 2015. The day featured addresses by members of Congress and Vice President Joe Biden.