Democrats will not cut Social Security benefits to balance the U.S. budget, House Minority Leader Nancy Pelosi said ahead of a White House budget meeting. "Do not consider Social Security a piggy bank for giving tax cuts to the wealthiest people in our country," Pelosi, D-Calif., told reporters on Capitol Hill Thursday after a White House-congressional debt-limit summit convened by President Barack Obama. Obama's private, 10 a.m. EDT Oval Office meeting with Pelosi -- who despite her reservations pledged "full cooperation" with negotiators -- will seek to soothe Democratic anxiety over Obama's proposal, officials said. Obama said after Thursday's meeting the eight Republicans and Democrats, including Pelosi, were still "far apart," but he expressed confidence they could agree on an ambitious deal to prevent the government from defaulting on its debt. He said White House and congressional staff members would work through the weekend and the congressional leaders would meet with Obama again at the White House Sunday. He said he hoped by then "the parties will at least know where each other's bottom lines are and will hopefully be in a position to then start engaging in the hard bargaining that's necessary to get a deal done." Key lawmakers and congressional officials said they thought the weekend work and Sunday meeting would prove pivotal, The New York Times reported. At the Thursday meeting, Obama put forward a far-reaching plan that would double GOP-proposed spending cuts to $4 trillion, including cuts to popular entitlement programs such as Social Security, Medicare and Medicaid, along with cuts at the Pentagon, in return for as much as $1 trillion in new revenues through a tax overhaul, officials said. House Speaker John Boehner, R-Ohio, said for the first time he was open to the new revenues. The money would be raised by closing loopholes and making other tax-code changes, possibly a thorough rewrite, officials said. The additional cash would be used to lower income-tax rates, so the government would still receive the same amount of money, they said. The proposal puts Obama and the congressional leaders at odds with major factions of their own parties, the officials observed. Democrats would be asked to cut social-safety-net programs and Republicans would be asked to do something that could look like raising taxes. Boehner stressed to reporters after the meeting "we are not going to raise taxes on the American people -- we are not going to raise taxes on the very people that we expect to re-invest in our economy." He also told reluctant Senate Republicans he enthusiastically endorsed Obama's call for a far-reaching plan, saying the nation's economic future required bold action, The Washington Post reported. Boehner told lawmakers over lunch he expected a deal would either come together quickly -- or collapse under the weight of partisan resistance, the Post said. White House spokesman Jay Carney stressed Thursday Obama would only consider Social Security changes that "would not slash benefits." Obama proposed, for instance, adjusting the price index that measures cost-of-living increases, which would whittle Social Security payments to recipients over time -- an idea Rep. Raul Grijalva, D-Ariz., called a deal breaker for many House Democrats.