Trump's outline comes as Republicans face increasing pressure to address rising health costs and a jump in insurance premiums after lawmakers let subsidies expire.
The White House is circulating a proposal that would extend subsidies to help consumers pay for coverage under the Affordable Care Act for two more years.
If Congress does not extend the tax credits as part of the government shutdown deal, hundreds of thousands of Californians who have the state's health insurance could see a 97% increase in monthly premiums.
President Donald Trump is making it clear he's unlikely to compromise with Democrats on their health care demands as a condition of ending the government shutdown.
Millions of Americans who bought into the ACA marketplace are now finding themselves caught in the crossfire of the government shutdown.
Republicans and Democrats remained at a stalemate on the government shutdown over the weekend as it headed into its sixth week, with millions of Americans starting to lose food aid benefits.