Without offering specifics on any threats, the lawmakers said Obama soon needs to develop a comprehensive strategy to crush the fighters.
"His foreign policy is in absolute free-fall," said Rep. Mike Rogers, a Michigan Republican who heads the House Intelligence Committee.
In another TV interview, Sen. Dianne Feinstein, the California Democrat who leads the Senate intelligence panel, said Obama is perhaps "too cautious" in his approach to combatting the Islamic State group.
"This is a group of people who are extraordinarily dangerous," Feinstein said. "And they'll kill with abandon."
The pair of lawmakers, who have access to some of the nation's most sensitive secrets and receive regular and detailed briefings from the nation's spy agencies, offered dire predictions of an attack on the United States or its European allies if the militants are not confronted.
"They have announced that they don't intend to stop," Feinstein said. "They have announced that they will come after us if they can, that they will, quote, 'spill our blood.'"
The threat, Rogers said, could include Americans who have trained with Islamic State fighters. He said there are hundreds of Islamic State-trained Americans who can return to the United States with their American passports.
"I'm very concerned because we don't know every single person that has an American passport that has gone and trained and learned how to fight," Rogers said.
Rogers said U.S. intelligence agencies were tracking the Americans who are known to have traveled to the region. Those people, he added, should be charged under existing laws that prohibit Americans from aiding terrorists.
An attack on a Western nation is the next goal for the group, Rogers said.
"ISIL would like to have a Western-style attack to continue this notion that they are the leading jihadist group in the world," Rogers said, using another name for the group.
The top Democrat on his intelligence panel, Rep. C.A. Dutch Ruppersberger of Maryland, was more skeptical about an attack from Islamic State fighters in the United States. He said more needs to be known before judging whether they plan to commit terrorist acts here any time soon. Islamic State fighters are taking over territory and their priority for the moment seems to be to hold on to that land rather than export violence.
"It is extremely urgent, but you don't just rush in," he said.
Sen. John McCain, an Arizona Republican who serves on the Senate Foreign Relations Committee, urged fast action and said Islamic State fighters "must be defeated, not contained."
"This is a direct threat to the United States of America," McCain said.
Feinstein said she has seen nothing that compares to the viciousness of the militants who have overrun large portions of Iraq, killed civilians and beheaded American journalist James Foley. The Islamic State group has financing, military structure and weapons unlike any other militants, she said.
Obama said Thursday that he did not yet have a strategy for dealing with the Islamic State organization, a remark that brought criticism from Democrats and Republicans. In an interview published early this year by The New Yorker, the president appeared to minimize the Islamic State group by comparing it to a junior varsity basketball team. The White House later said he was speaking about a different threat posed by a range of extremists across the world.
Feinstein said she thought the basketball analogy was wrong — "I think it's a major varsity team" — but would not say whether she thought not having a strategy yet, as Obama acknowledged on Thursday, projected weakness from the White House.
"I think I've learned one thing about this president, and that is he's very cautious," she said. "Maybe in this instance, too cautious. I do know that the military, I know that the State Department, I know that others have been putting plans together. And so hopefully, those plans will coalesce into a strategy."
Feinstein spoke to NBC's "Meet the Press." Rogers appeared on "Fox News Sunday." Ruppersberger was on CNN's "State of the Union." McCain was interviewed on CBS' "Face the Nation."