Democrats are looking to provide states with some financial aid, extend unemployment benefits beyond the 26 weeks offered by most states and to get some more money for food stamps.
For now, lawmakers are putting aside the bitter partisanship that dominated last year's session and which resulted in near-gridlock over spending, taxes, health care and the Iraq war.
"I am encouraged and share the president's view that we need prompt bipartisan action to strengthen our economy," said Senate Majority Leader Harry Reid.
Only a day earlier, the Nevada Democrat had expressed some disappointment with the results of a telephone conference between Bush and congressional leaders.
U.S. Sen. Charles Schumer, a New York Democrat, said after Bush's remarks on Friday that the president needed to accept some spending as part of the package.
"We want a balanced package of tax rebates for the middle class and spending stimulus that jump-starts the economy quickly," Schumer said at a news conference.
Bush predicted that an agreement could be worked out soon. The administration and lawmakers say the outlines of plan could be clear by Bush's State of the Union address to Congress on January 28.
"I believe we can come together on a growth package very quickly," Bush told reporters as he visited a lawn mower factory in Maryland on Friday.
Most of the major White House contenders have unveiled proposals for the economy but they differ widely on specifics, highlighting the challenges in getting a bipartisan agreement.
Sen. Hillary Clinton, who has proposed a $110 billion plan that would target poor and middle-class people, said Bush's approach would shortchange struggling families.
"I don't think it does enough," she said in Las Vegas.
Meanwhile, Republican Sen. John McCain, campaigning in South Carolina, expressed wariness about some Democratic ideas for a stimulus, especially those focusing on spending.
"I want to see where that money is going to come from," said McCain, who laid out a proposal on Thursday for cuts in corporate tax rates and incentives for companies to invest in new equipment and research.
