At his first White House news conference in three months, Obama also called on Congress to renew a payroll tax cut that took effect on Jan 1, one of several steps he said lawmakers can take quickly to help reduce 9.1 percent unemployment.
Although he declined to announce support for legalizing gay marriage, he defended his record on rights for homosexual Americans, saying he had done more to advance their cause than any of his 43 presidential predecessors.
On the deficit and economy, Obama said both parties must be prepared to "take on their sacred cows" as part of the negotiations, with Democrats accepting cuts in government programs.
At the same time, he said any agreement must include increased government revenue. Attempting to blunt Republican criticism, he said he also wants to extend existing middle class tax cuts.
"The tax cuts I'm proposing we get rid of are tax breaks for millionaires and billionaires, tax breaks for oil companies and hedge fund companies and jet owners," he said.
"That's not radical," he said, adding quickly that a bipartisan agreement is possible to cut deficits, raise the government's $14.3 trillion debt limit and avert a threatened financial crisis. He said a plan must be in place by Aug. 2, a date he called "a hard deadline."
Obama's last previous full-fledged news conference was in March. In the intervening months, the economic recovery has slowed, the president has announced a plan to begin withdrawing U.S. combat troops from Afghanistan and the administration has joined an international military coalition working to prevent the rout of rebels hoping to topple Libyan leader Moammar Gadhafi.
The president stepped to the podium not long after the International Monetary Fund publicly urged lawmakers to raise the U.S. debt limit, now $14.3 trillion, and warned that failure to do so could produce a spike in interest rates and "severe shock to the economy and world financial markets."
The IMF recommended a long-term strategy for reducing red ink, warning that cutting deficits too quickly could slow the weak recovery of the U.S. economy.
The budget deficit is projected to reach a record $1.4 trillion for the current fiscal year, which ends Sept. 30.
Republicans in Congress have been insistent in recent days that any deficit reduction be limited to spending cuts, including reductions in benefit programs such as Medicare and Medicaid, and exclude additional revenues.
In remarks made during the day, Senate Republican leader Mitch McConnell of Kentucky said Obama "said as recently as six months ago that keeping taxes where they are enables businesses to hire more workers. In other words, that raising taxes leads to fewer jobs. So he can call for tax hikes. But he can't call for tax hikes and job creation. It's one or the other. `'
Obama said talks led by Vice President Joe Biden had "identified more than $1 trillion worth of spending cuts already. But everyone also know that we need to do more to close the deficit," he added, citing a goal of $4 trillion.
In his opening remarks, the president called on lawmakers to renew a 2 percentage point cut in Social Security taxes in effect since Jan 1, pass trade agreements with Panama, South Korea and Colombia and overhaul of the nation's patent laws.
On Libya, the president defended American participation in the NATO military action, saying the U.S. had carried out a "narrow mission in an exemplary fashion" against a tyrant who was threating to "massacre his people."
"We have not seen a single U.S. casualty," he said. "There's no risk of additional escalation. This operation is limited in time and in scope."
Defending his record on gays, he pointed to eliminating the ban on openly gay men and women serving in the military, a policy known as "don't ask, don't tell," as well as ordering the Justice Department not to defend a law that defines marriage as between a man and woman.