(CNN)President-elect Donald Trump is putting the finishing touches on an Obamacare replacement plan that aims to provide "insurance for all," he told The Washington Post.

Also, he will demand that drug companies negotiate directly with Medicare and Medicaid and lower their prices, saying they will no longer be "politically protected."

Trump did not reveal any details of how he'd accomplish this daunting task, noting that he is waiting for his health secretary nominee, Tom Price, to be confirmed. Price is appearing before the Senate Health, Education, Labor & Pensions Committee on Wednesday, but his hearing before the crucial Senate Finance Committee has yet to be scheduled.

Trump's weekend interview with The Washington Post comes just after Congress took its first steps to dismantle President Barack Obama's landmark health care reform law. The House on Friday followed the Senate in approving a budget resolution that would repeal major portions of the Affordable Care Act. Committees in both chambers will now work out the details of repealing and replacing the law.

However, after nearly seven years of vowing to repeal Obamacare, Republicans are fracturing over how to do actually go about doing it. Some want to slow down the repeal effort until a replacement plan is unveiled.

Trump is making some big promises: His insurance reform will cover more people and cost less money.

"We're going to have insurance for everybody," Trump told The Washington Post. "There was a philosophy in some circles that if you can't pay for it, you don't get it. That's not going to happen with us."

"[They] can expect to have great health care. It will be in a much simplified form. Much less expensive and much better," he said.On the campaign trail, Trump promised he would "take care of everybody" and that Americans can't let "people die on the street." He also said he would press for Medicare to be allowed to negotiate drug prices. He acknowledged all these were not very Republican things to say.

Congressional Republicans have shied away from saying how many people their replacement plan will insure, preferring to use the term "universal access" versus the Obamacare's "universal coverage" goal. Some 20 million people have gained coverage under Obamacare and the nation's uninsured rate has dropped to 8.9% in the first half of 2016, from 14.4% in 2013, before the Affordable Care Act's exchanges opened and Medicaid expansion took effect.

Trump's promises could also set up potential conflicts between him and his health secretary nominee. Price, a Georgia representative who chairs the House Budget Committee, has authored his own replacement plan that does not have universal coverage as its primary goal.

Trump did not say how his proposal compares to that of House Speaker Paul Ryan, who has also promised to unveil a detailed replacement plan in coming weeks.

Republicans have long slammed Obamacare, saying its high premiums and deductibles leave enrollees feeling like the don't have insurance. They have vowed to lower the cost, primarily by lifting Obamacare's insurance regulations that require carriers to provide comprehensive benefits.

Ryan and Price have unveiled frameworks for replacement plans that rely on tax credits based on enrollees' age, not income. However, health policy experts have said those credits will have to be generous in order to make coverage affordable. And that could run afoul of Republicans' promise to lower federal spending on health care.