"But what we can't do is let very modest differences get in the way of the overall package moving forward swiftly," Obama said on Monday.
The bill, which could amount to almost $900bn when it is finished, will direct aid to cash-strapped states to boost employment, consumption, and social spending.
Mitch McConnell, the senate Republican leader, said the bill would need to be "dramatically different" from the one that the House of Representatives passed last week but insisted Republicans were not stalling the bill.
"We're not trying to prevent a package from passing. We're trying to reform it," he told journalists on Monday.
"We need to make sure that we're not borrowing money to spend on projects that are not going to stimulate the economy," he added, voicing Republican complaints the bill contains too much spending on programmes supported by Democrats.
John McCain, the former Republican presidential candidate defeated by Obama, also told CBS News: "There's too much spending, too much unnecessary spending, not the right kind of tax cuts and no endgame."
Al Jazeera's Rob Reynolds in Washington says there is particular controversy over a "Buy American" provision in the bill which would require all iron, steel and other materials used in construction projects to be US-made.
'Urgent situation'
This has led to some politicians expressing concerns that other nations such as China and India could retaliate over what they see as protectionism, and Obama has reportedly said he would take the issue into consideration, our correspondent adds.
Obama also said on Monday he was setting up a board that would review the spending of the funds contained in the stimulus package, the Associated Press news agency reported.
Obama also held a fresh round of talks with congressional leaders on Monday to try and avoid deadlock over the measures.
"The thing I want all of them [members of congress] to remember, and the thing I am thinking of every single day, is the thousands of people being laid off from their jobs right now," he said in an interview with the NBC television network.
"They can't afford politics as usual and old habits are hard to break, but now is the time to break them because we have an urgent situation."
Global turmoil
Democrats hold a majority in the senate, but do not have the 60 seats needed to overcome a "filibuster", a parliamentary stalling move that would stop the plan from going to a vote.
Every Republican legislator voted against the bill in the House, amid concerns that the package included too little in tax cuts and too much in spending.
They said the plan would burden the government with new budget obligations and contains funds for non-relevant items.
One such item, such as $75 million for smoking prevention programmes, has already been dropped and Robert Gibbs, the White House press secretary, said the remaining items that have drawn criticism amount to less than one per cent of the entire package.
Debate over the package has continued. A US government report last week showed that in the last three months of 2008 the national economy declined 3.8 per cent, marking its worst contraction in 25 years.
The rate could accelerate to five per cent in 2009.
Obama also said on Monday that some US banks could still go out of business after the subprime mortgage crisis and global financial turmoil.
"It is likely that the banks have not fully acknowledged all the losses that they're going to experience. They're going to have to write down those losses. And some banks won't make it,'' Obama told NBC television.