"Hope springs eternal," Obama said about whether the White House and Congress can act to avoid the sequester before it goes into effect March 1.
"I will just keep on making my case, not only to Congress, but more importantly to the American people, to take a smart approach to deficit reduction and do it in a way that doesn't endanger our economy and endanger jobs," Obama said during a media availability with Japanese Prime Minister Shinzo Abe.
Obama said he's been clear about an alternative that would be a balanced approach of spending cuts and revenue producers, such as closing tax loopholes.
"So I will continue to have conversations with members of Congress both while they're gone [this week in recess] and when they get back next week," Obama said. "My hope is that we could see a different course taken by Congress. This should be a no-brainer."
Unlike the debt ceiling crisis, the sequester going into effect won't threaten the world financial system, Obama said.
"It's not like the equivalent of the U.S. defaulting on its obligations," he said. "What it does mean, though, is that if the U.S. is growing slower, then other countries grow slower because we continue to be a central engine in world economic growth."
On Thursday, White House spokesman Jay Carney said Obama "had good conversations" with the two Republican leaders but offered no details. Spokesmen for Boehner and McConnell didn't expand on the calls either.
A Boehner aide told CBS News "the last substantive conversation" Boehner had with Obama was Dec. 28, just before a New Year's Eve "fiscal cliff" deal. A McConnell spokesman said Obama's last outreach before Thursday was New Year's Eve.
Republicans interpreted the latest outreach as a public relations stunt and not a new basis for negotiation, CBS News said.
The cuts -- established as part of the 2011 deal to raise the federal debt limit -- represent a small slice of the government's annual $3.5 trillion budget, and big-ticket programs such as Social Security and Medicare benefits are exempt from them.
The cuts are expected to be phased in gradually over several months.