Cath Turner, Al Jazeera's correspondent on Capitol Hill in Washington DC, said Saturday's debate was concentrating on amendments that Republicans were putting forward.
"Republicans want more changes to the bill. What this does is take up a lot of time," she said.
"There could be a vote on Tuesday - if the bill gets 60 senate votes it will go [back] to the House [of Representatives]. Obama has said he wants that bill ready on his desk to sign by Friday.
"In his radio address, Obama said much of the money will go to key areas he has campaigned about, such as education and new jobs in healthcare. He also wants to pump a lot of money in to federal programmes such as renewable energy."
Friday's deal came after days of wrangling over the package between Democrats and Republicans in the senate.
Rahm Emmanuel, Obama's White House chief of staff, and Harry Reid, the senate majority leader, have held talks with senators on Capitol Hill in a bid to attract the support of enough Republicans to give the measure the needed 60-vote majority.
On Friday, Obama condemned Republican opposition for delaying the plan, saying it was "inexcusable and irresponsible" to delay a vote on the bill further.
But Republicans - and some moderate Democrats - complained that Obama's original bill was too large, contained insufficient tax cuts and was filled with spending on unnecessary projects.
The smaller bill allocates around 42 per cent of the money to tax cuts and 58 per cent new government spending, whereas before only about one-third of the bill was set aside for tax cuts, sources said.
"American families are doing their best to balance their own budgets and pay their mortgages," Michael Steele, chairman of the Republican National Committee, said in the party's radio address on Saturday.
"The fastest way to help those families is by letting them keep more of the money they earn."
The US House of Representatives passed an earlier version of the bill last Wednesday.
US government data released on Friday has piled further pressure on politicians to act quickly to fix the country's faltering economy.
Labour department figures showed on Friday that 598,000 jobs have been lost in January, the largest cut in 34 years.
The unemployment rate also surged to 7.6 per cent.
The White House said the figures were evidence that the US economy was "contracting greatly".
The US economy is in a recession following months of market turmoil sparked by a subprime mortgage crisis, tight credit conditions and slumping global markets.