Sen. Max Baucus (D-Mont.) will redirect about $28 billion in his healthcare bill to make insurance more affordable for middle-class families and reduce a new tax on insurance companies.

Baucus announced the changes in interviews with The New York Times and Wall Street Journal.

The changes were spurred by a Congressional Budget Office analysis that found Baucus's original bill would reduce the deficit by $49 billion over 10 years. Baucus has decided to instead spend $28 billion of those savings to make the bill more palatable to centrists.

Baucus's original plan to levy a 35 percent tax on insurance companies for high-end, "Cadillac" policies led some lawmakers to worry that insurance companies would pass the costs on to consumers.

In addition to reducing that tax, Baucus's changes will provide more subsidies to middle- and lower-income Americans to help them purchase coverage. The bill mandates that most Americans buy coverage or pay a fine.

"Affordability — that, I think, is the primary concern," Baucus told the Times. “We want to make sure that if Americans have to buy insurance, it’s affordable."

Both of these changes have been sought by centrist Democrats and Sen. Olympia Snowe (Maine), the Republican seen as most likely to support a reform package.

The Senate Finance Committee will start marking up Baucus's legislation Tuesday.