The ball was set rolling last week with Ed Royce, Republican chairman of the House of Representatives Foreign Affairs Committee and a fellow House member George Holding writing to House Speaker John Boehner with the suggestion.
"As you know, India is a critical partner of the United States. In every aspect - whether it be in political, economic or security relations - the United States has no more important partner in South Asia," they wrote.
Following up on the letter, the US India Political Action Committee (USINPAC), which calls itself the voice of Indian- Americans, has launched a "state-by-state grassroots campaign" to win support for a Congressional invitation to Modi.
Three former Indian Prime Ministers, Rajiv Gandhi, Atal Bihari Vajpayee and Manmohan Singh have all been accorded this honour, noted USINPAC Chairman Sanjay Puri thanking Royce for his move.
USINPAC activists and chapter leaders in North Carolina, Indiana and New York among others have actively reached out to members of Congress in their states to win their support for such a Congressional invitation, USINPAC said.
Bridging Nations Foundation, a nonprofit policy and advocacy organization founded by Indian-American entrepreneur Prakash Ambegaonkar, to "promote shared prosperity by developing international dialogue through collaboration and learning," has also initiated a similar move.
By granting "Prime Minister Modi the honour of addressing a joint meeting of Congress, the US would show to the Indian people and the world our sincerity in rebooting and elevating US-India relations,' it said.
The foundation urged Indian-Americans to "pick up your phone to contact your own congressmen" and request them to write to Boehner in support of the invitation.
The Speaker's office has not yet announced a response to the two lawmakers' letter, but an invitation to Modi is considered highly likely given how US leaders from President Barack Obama down have reached out to the Indian leader since his resounding victory.
The previous Bush administration had revoked Modi's tourist/business visa in 2005 for his alleged inaction during the 2002 Gujarat riots under a 1998 US law barring entry to foreigners who have committed "particularly severe violations of religious freedom".
Though late in reaching out to Modi in the run up to the elections, the US quickly made amends with Obama congratulating him on his victory and inviting him to visit Washington. Modi has accepted the invitation, though no dates have been announced.