Donald Trump believes that his health plan will get support from Democrats. | Getty Trump promises 'insurance for everybody'

President-elect Donald Trump vowed he'll soon unveil a new plan to replace Obamacare that will provide "insurance for everybody," according to an interview with the Washington Post published Sunday night.

Trump said that his plan is "very much formulated down to the final strokes. We haven’t put it in quite yet but we’re going to be doing it soon." He didn't give specifics but did say that the plan would provide a "much simplified [and] much less expensive" form of coverage to Americans currently covered through the Affordable Care Act.

Trump added that the plan would not cut Medicare -- and that he plans to separately force drug companies to negotiate with Medicare as well as Medicaid on drug price. Most Democrats back Medicare drug negotiations, but Republicans have opposed them.

He also believes that his health plan will get support from Democrats. "I won’t tell you how, but we will get approval," Trump said.

Given how far the two sides are on health policy -- Democrats wanting universal coverage and Republicans emphasizing "access" and cost -- it's not clear how Trump plans to bridge the bitter differences. But Trump said he will unveil the plan alongside House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell after HHS Secretary-designate Tom Price is confirmed.

Price must still undergo a confirmation hearing with the Senate Finance Committee, which has not yet been scheduled.