After putting off the request in 2012 because of the U.S. presidential election, the U.S. Treasury has sought to tuck the provision into several bills since March.
The administration's requests, however, have been met with skepticism from some Republicans, who see them as tantamount to approving fresh funding in a tight budget environment.
Some lawmakers have also raised concerns about how well the IMF is helping struggling economies in Europe and the risks attached to IMF loans, suggesting Congress is in no hurry to approve any changes
India's Finance Ministry did not immediately respond to requests for comment. But an official at the ministry, who has been dealing with multilateral institutions including the IMF, said India was "disappointed" at the Congress lack of action.
(Read more: Has the IMF got it wrong on emerging markets?)
The official declined to be identified because he was not authorized to talk to the media.
A South Korean Finance Ministry official, who declined to be identified, said: "While we appreciate the U.S. government's efforts, we regret the fact that the proposed funding measure fell through in Congress at the last minute.
"IMF quota reform is an important matter to address and we hope that the matter will be discussed at the G-20 level with the end-January deadline approaching."
Developing nations have longed viewed the IMF with suspicion for promoting disastrous privatizations that complicated the transition from communism for some emerging nations in the early 1990s, and for pushing budget cuts that exacerbated debt crises in Asia and Latin America a few years later.
(Read more: Emerging markets may become new force in euro rally: Goldman Sachs)
That suspicion has been compounded by a power structure that dates to IMF's founding in 1944. The structure was shaped by the victors of World War Two - the United States and Europe.