For months, the private-equity industry has fought hard to reduce a proposed $18 billion tax hike — but their efforts may be falling short, a source said.

Senate Finance Committee Chair Max Baucus, the main focus of industry lobbying, is more interested in getting the overall Tax Extenders Bill through Congress than he is at pleasing the PE industry, a well-placed source said.

The House voted May 28 to treat half of the typical 20 percent commissions PE tycoons pocket from profits, called carried interest, at the higher ordinary income rate. That rate would jump to 75 percent in 2013. The plan would raise roughly $17.7 billion over 11 years.

Baucus this week proposed reducing the 2013 rate to 65 percent, a move that would save PE tycoons $3 billion. But Baucus may withdraw his proposal to satisfy House Ways and Means Committee Chair Sandy Levin, who has not indicated he is willing to back off the original proposal, the source said.

“I think the [cost of the bill] is the big issue; carried interest [though he would like to reduce the hit] is just an irritant,” the source added.

The Senate and House are expected to vote on the matter next week.