"That's good news," President Obama said of passage when told about it during a town hall meeting in Fort Myers, Fla.
But he also noted: "We've still got a little more work to do." ( .)
The bill now faces what could be contentious negotiations with the House, which passed a different version of the legislation, one that includes fewer taxes and more spending than the Senate version.
Majority Leader Harry Reid, D-Nev., vowed to send a finished bill to Mr. Obama's desk "as soon as possible."
Just three Republicans helped pass the plan on a 61-37 vote and they're already signaling they'll play hardball to preserve more than $108 billion in spending cuts made last week in Senate dealmaking. Mr. Obama wants to restore cuts in funds for school construction jobs and help for cash-starved states.
Those cuts are among the major differences between the $819 billion House version of Mr. Obama's plan and a Senate bill costing $838 billion. Mr. Obama has warned of a deepening economic crisis if Congress fails to act. He wants a bill completed by the weekend. (Read more about what's next.)
Differences have to be worked out but both bills include tax cuts for almost all working Americans, vast new spending on building new roads and bridges, investing in new energy projects and clean fuels, aid to financially strapped states and help for the unemployed including higher benefits and help in paying premiums to keep their health insurance, reports CBS News correspondent Bob Fuss.
The three Republicans who voted for the package are Sens. Susan Collins and Olympia Snowe of Maine and Arlen Specter of Pennsylvania. They joined all Democrats and Independents Joe Lieberman of Connecticut and Bernie Sanders of Vermont.
CBS News correspondent Chip Reid reports that in case his vote was needed, Ted Kennedy interrupted treatment for a brain tumor to be on the Senate floor, where he was greeted by Robert Byrd, his friend of more than 45 years.
Mr. Obama's choice to be commerce secretary, Republican Sen. Judd Gregg of New Hampshire, did not vote, keeping his commitment not to participate in Senate business or votes while his confirmation is pending. All other Senate Republicans voted against the bill.
There is also a vacant seat in the Senate due the ongoing recount battle between Al Franken and Norm Coleman in Minnesota.
Not a single Republican voted for the bill in the House.
"I'm reticent to get into the negotiating," White House press secretary Robert Gibbs told NBC's "Today" show Tuesday. "I will tell you this, the president is willing to do whatever it take with Democrats or Republicans to get something on his desk." He said the American people need the help "right now."
Meanwhile, the Treasury Department announced an .
Treasury Secretary Timothy Geithner, who was spelling out new bailout details for the nation's lenders, said in remarks prepared for the announcement, "Right now, critical parts of our financial system are damaged.
That plan includes a public-private partnership of over $1 trillion to help strengthen banks. Added to the congressional stimulus plan, which aims to get Americans spending again, the total of the combined efforts could easily pass $2 trillion.
Geithner said the bailout plan would lead to "cleaner and stronger" bank balance sheets by imposing tough new standards and using government and private incentives to get the banks lending again. ( .)
Tuesday afternoon, CBS News Producer John Nolen reports, Reid led a preliminary meeting in his office to discuss where things stand with the stimulus bill.
Three representatives from the White House were present: Chief Of Staff Rahm Emanuel, Congressional liaison Phil Schiliro and Office of Management and Budget Director Peter Orszag.
The Senators present included Reid, Finance Committee Chairman Max Baucus, Nebraska Sen. Ben Nelson, Lieberman, and Collins and Snowe, two of the Republicans who supported the bill.
Around 5:00 PM, Emanuel and Reid went to House Speaker Nancy Pelosi's office for about 25 minutes. They then returned to Reid's office to continue meeting.
In total, Emanuel has already been in discussions on Capitol Hill for almost four hours.
There is not yet word on when the stimulus conference will hold its first official meeting.