President Obama Says 'Obamacare' Will Survive Beyond His Presidency

“It may be called something else. And as I said, I don't mind," Obama said.

"It may be called something else. And as I said, I don't mind. If in fact the Republicans make some modifications, some of which I may have been seeking previously, but they wouldn't cooperate because they didn't want to -- make the system work, and relabel it as Trumpcare, I'm fine with that," he said in an exclusive interview on “This Week” Sunday.

He also noted that progress has been made during his time in office on access to health care.

"When it comes to health care, the gains that we've made are there. Twenty million people have health insurance that didn't have it before. The uninsured rate is the lowest it's ever been," Obama said.

He warned Republicans against undoing that progress just because his name is attached to it.

"It is true theoretically that all that progress can be undone, and suddenly 20 million people or more don't have health insurance," Obama said on “This Week.” "I think Republicans now are recognizing that's -- may not be what the American people, including even Trump voters, are looking for.”

"Don't undo things just because I did them. I don't have pride of authorship," he added.