The Hill newspaper's report was in reaction to a press release by the US-India Political Action Committee which had said the Chair of the House International Relations Committee Henry Hyde said in a private meeting that he plans to mark up legislation on or before June 21.
The USINPAC had also touted Hyde's support for the deal saying that his backing is "critical to the successful passage of the deal."
But The Hill quoted a spokeswoman for Hyde as saying that the lawmaker "...has serious concerns regarding the proposed civil nuclear agreement."
"The Chairman reiterated his support for the President's initiative in reaching an agreement with India, however he did tell the US-India PAC that he will be working with the administration and Mr Lantos to craft a bipartisan piece of legislation that supports the President's effort to strengthen ties with India," said Kristi Garlock, Hyde's committee spokeswoman.
Hyde is in the process of crafting his own bill, she said.
"It is an important priority that has support, and we hope and expect to move legislation to the floor before the August recess," said Kevin Madden, spokesman for House Majority Leader John Boehner (Republican from Ohio).
N-deal: Council of Foreign Relations urges approval
But Madden added, "No decisions have been made about when it will be considered on the floor calendar yet."
The Hill report also says that the Senate Majority Leader Bill Frist said he is relying on Senator Richard Lugar, chairman of the Foreign Relations Committee, to take care of it in the committee.
The Chair of the Senate Foreign Relations Committee backs the accord but has indicated that he may seek to add some conditions.
"I think it is certainly the intent of the President and the Senate for (the legislation) to pass sometime in 2006," said Andy Fisher, spokesman of the Committee told The Hill.
What is being pointed out is that the Senate has a crowded schedule on its hands having just finished with debating a constitutional ban on gay marriage. But it has still got to get through with a flag-burning amendment and a tax package that has strong bipartisan opposition.
Adding to this the Senate has to consider the 2007 defence authorisation bill, and both the House and the Senate still have to deal with the 2006 emergency supplemental.
The recognition is there that the United States-India nuclear deal will not kick up a partisan fight because it has not been seen as a Republican vs Democrat issue, still The Hill quoted an aide as saying that Democrats are not willing to give Bush "carte blanche."
"The problem is that the administration's initial proposal was to enunciate some general principles and for Congress to pre-approve those," a Congressional aide said, adding that after the initial pre-approval, Congress would have a chance to overturn the deal, but only with a two-thirds vote.
"It is complicated procedurally and the administration is eager to move on," the aide was quoted as saying.
"They think some indication of Congressional support is going to make a difference in terms of what they are going to do with the Indians. The Indians have some tough decisions to make, and the idea is that if Congress is going to do something they will be likely to make the changes," the unnamed aide told the newspaper.
The Hill noted the fact that the ranking Democrat in the House International Relations Committee, Tom Lantos, is continuing to circulate his version of a two-step process enunciated a few weeks ago -- that Congress will act on a stepped up and accelerated process once it has been presented with the technical nuclear accord and India's agreement with the IAEA on safeguards.