Image copyright EPA Image caption Manchin and Sinema have reached an agreement on the bill
The Democratic senator who has been negotiating a debt relief bill with West Virginia and Arizona co-sponsored the proposal on Monday.
The bill would provide $24bn (£19bn) in federal support to homeowners affected by the floods.
Democrat Senator Chuck Schumer said Democrats were open to negotiating changes to the Republican-sponsored legislation with the pair.
He added that he hoped the Democrats and Republicans would reach an agreement by Christmas.
“The bread and butter was the funding of the essential recovery efforts needed,” he said.
“We then went to the regulatory side. The Republicans were so determined to cut rules that it’s affected flood insurance.”
He also confirmed a three-way deal with Democrats and Republicans to end a government shutdown crisis.
Image copyright EPA Image caption Republican Representative Mark Walker said a deal had been reached
Republican Representative Mark Walker of North Carolina and Democratic Representative Kyrsten Sinema of Arizona have announced an agreement on the bill, which will be negotiated by Democratic senators from those states.
Under the bill the federal government would provide $24bn (£19bn) in assistance to homeowners to rebuild after last month’s torrential rains.
The total cost would be divided between the federal government and state and local governments.
Earlier this week it was revealed that billions of dollars in reconstruction money may not be spent following the floods in 2018 because the programme is about to expire in December.
Floods in West Virginia and Arizona have already destroyed hundreds of homes and businesses.
The floodwaters now are receding in both states. About five hundred homes and more than one thousand businesses have been destroyed in West Virginia and more than 300 homes and businesses have been destroyed in Arizona.