Mr Cheney said in Washington that the deal was "one of the most important strategic foreign policy initiatives of President Bush's second term".
Reuters has reported that legislation prepared for action next week by a key House of Representatives committee would require India to strongly support US efforts to halt Iran's nuclear ambitions and would bar lawmakers from amending the formal peaceful nuclear cooperation agreement still under negotiation by Washington and New Delhi.
The draft bill, which was obtained by Reuters, is "much closer to the Bush administration's initial cut than things that were being talked about" earlier by some lawmakers, said a congressional analyst who closely followed the drafting process.
If supported, the deal would give India access to US nuclear technology.
It reverses US policy, which had restricted nuclear co-operation since India tested a nuclear weapon in 1974.
The agreement was finalised during US President George W Bush's visit to India in March.
Under the deal, energy-hungry India will get access to US civil nuclear technology and open its nuclear facilities to inspection.
"We hope Congress will move quickly to enact legislation that enables our two nations to move forward on this important agreement without delay," Cheney told a meeting of the most influential American and Indian business group in Washington
The final vote on the proposed agreement is not expected till the middle of July.
Before that, next week, on 27 and 28 June, the proposed deal must go through a rigorous assessment process by the powerful US Senate Foreign Relations Committee and the House International Relations Committee of Congress.
Critics of the deal say it sends the wrong message to countries like Iran, whose nuclear ambitions Washington opposes.
They believe that at a time when stand-off with North Korea and Iran is deepening, the civilian cooperation deal between US and India severely undermines the global nuclear non-proliferation regime.
Opponents of the deal also believe that by creating an exception for India, US is rewarding a country who has so far refused to sign up to the international nuclear Non-Proliferation Treaty (NPT).
Diplomats also say there are deep reservations in the 45-nation Nuclear Suppliers Group, which also must approve the agreement.
The Bush administration has responded to the criticism by pointing out that under the deal, India will be obliged to open up its civilian nuclear sites to international safeguards under the UN nuclear watchdog, the IAEA.