The bill has more than $300 billion in tax credits for producers and buyers of low carbon energy, including wind and solar power and existing nuclear plants.
Manchin supports carbon capture, and wants to make the subsidies easier to secure.
After Manchin opposed an initial methane fee, Democrats softened it to phase in fees on drillers starting at $900 per tonne of emissions instead of $1,500.
Democratic Representative Pramila Jayapal, a progressive, suggested in a press call that Biden could advance methane fees through executive action.
Several cities, including most recently New York, have embraced proposals for new buildings to use electricity for heating and cooking instead of gas-burning appliances.
That tactic could require achieving 60 votes in the evenly divided Senate.