WASHINGTON — Standing in the Rose Garden, where he once marked the Paris climate accord, celebrated the Supreme Court decision saving his health care law and unveiled the Iran nuclear deal, President Obama promised on Wednesday to “root for” Donald J. Trump, even though Mr. Trump has vowed to topple those and other pillars of Mr. Obama’s legacy.

“Everybody is sad when their side loses an election,” the president declared. “But the day after, we have to remember that we’re actually all on one team. This is an intramural scrimmage.”

For Mr. Obama, however, this scrimmage could result in the reversal or dismantling of several of his most cherished achievements — laws and agreements that required years of negotiation, heavy doses of political capital, and, in some cases, a stroke of luck.

The White House acknowledged that Mr. Obama’s signature legislation, the Affordable Care Act, was in genuine jeopardy. Mr. Trump has vowed to repeal it as one of his first acts in office, and a Republican-controlled Congress will prod him to do so. Josh Earnest, the White House press secretary, said Mr. Obama would lobby Mr. Trump to keep it in place — an effort that suggests Mr. Obama believes that Mr. Trump can be persuaded on certain issues.