Local government minister Mr Healey told MPs on Friday they could vote on the strategies that will govern decisions on major projects, like nuclear power stations before they are referred to the Infrastructure Planning Commission.
Sixty-three Labour MPs have indicated a willingness to rebel by signing an early day motion expressing concern about the measure.
Labour backbencher Clive Betts is leading the rebellion with an amendment to the Planning Bill that would ensure the power to make final decisions remain with a minister.
He said there was widespread dissatisfaction among backbench Labour MPs over the proposals, adding that he had yet to hear a “credible explanation” from ministers to justify their stance.
Mr Betts said: “It is my intention to push ahead with the amendment. I am supportive of the Planning Bill we do need a new way to deal with major projects that does not take five or 10 years.
“We need safeguards though, the most important of which is that the final decision rests with the secretary of state, not an unelected commissioner.”
Rynd Smith, head of policy at the Royal Town Planning Institute, backed Mr Healey’s compromise while calling for more community involvement in major planning decisions.