The plan that would give an unlimited deduction on federal returns for state and local taxes under a certain income.
House Democrats have proposed increasing the cap to $80,000 from $10,000 through the end of the decade.
Concerns mount that wealthy Americans are using retirement accounts as powerful tax-avoidance vehicles.
President Joe Biden has pledged that the bill won't add to the deficit.
The party's progressive wing has resisted changes they say are too beneficial to billionaires.
Yet another attempt to compromise on taxation and spending proposals is being floated by Congress.
Sen. Bernie Sanders said he could support unlimited SALT deductions only for those earning under $400,000 a year.
The plan has become the leading option for dealing with the state and local tax deduction limit.
Talks were centering on a two-year suspension of the cap.
It's far from clear what measures will make the final cut.