Obama sought to remind conservatives that they have cautioned against "judicial activism" for years.
"Well, this is a good example," he said, of the dangers of "an unelected group of people [who] would somehow overturn a duly constituted and passed law."
GOP Sen. Orrin Hatch (Utah) shot back that Obama shouldn't try to blame the court and voters for rejecting what Obama's reelection campaign has touted as his "signature domestic achievement."
"It must be nice living in a fantasy world where every law you like is constitutional and every Supreme Court decision you don't is 'activist,' " Hatch said in a statement.
"It is not unprecedented at all for the Supreme Court to declare a law unconstitutional; they do that on a regular basis, so it's not unprecedented at all," Smith said. "What is unprecedented is for the president of the United States trying to intimidate the Supreme Court."
The Supreme Court's decision on the 2010 healthcare insurance reform legislation is not expected to become public until sometime this summer. The White House has maintained that it expects the court to rule the law constitutional, while GOP leaders have refused to speculate but say they hope the bill, whether in part or entirely, is struck down.