"This is about people. This is not about politics, it's not about Washington," Obama said at a town-hall-style meeting at a Nashville elementary school.
"And so my hope is is that on a bipartisan basis, in places like Tennessee but all across the country, we can now focus on ... what have we learned, what's working, what's not working."
Last week, the court emphatically rejected a legal challenge to the health law that threatened to strip insurance subsidies it made available to more than 6 million Americans.
That would have reversed a historic coverage expansion that began in 2014 when the health law was fully implemented.
In the first quarter of this year, 11.9% of adults in the U.S. lacked insurance, down from 18% in the third quarter of 2013, before the expansion began, according to Gallup.
The Supreme Court decision has energized supporters of the health law and prompted Obama to repeatedly hail its successes in recent days.
More than six in 10 Americans approve of last week's Supreme Court decision, according to a new national poll from the nonprofit Kaiser Family Foundation. That is twice the number that disapprove.
But Americans remain deeply divided over the law, as they have been since it was enacted. And more than three-quarters of Americans said they expect more major battles over it, the poll found.
Tennessee is among 21 states, mostly led by
Obama declined to jump into the healthcare debate in Tennessee on Wednesday, but he urged Republican legislators to propose alternatives if they do not like the health law's system of expanding coverage.
"I have no pride of authorship here," the president said. "If there is a better way of doing it, let me know."
Republican governors in several states, including Arizona, Indiana, Iowa, Nevada, New Mexico and Michigan, have backed the Medicaid expansion. Several are experimenting with more conservative approaches, including requiring poor patients to pay premiums and co-pays for medical care.
Even New Jersey Gov. Chris Christie, who this week announced his bid for the Republican presidential nomination, and Ohio Gov.
Several more red states are actively discussing Medicaid expansions, including Alaska and Utah.