The house package devotes more money to states, local governments and schools while the senate's version puts a greater emphasis on tax cuts, in response to complaints from Republicans.
Obama hailed the bill's senate passage on Tuesday as "good news".
Al Jazeera's Rosiland Jordan in Washington said it could be next week before US politicians managed to agree on what remained in the package.
The bill's passage also came as Obama held the second of his "town hall" meetings with American citizens, in which he reinforced his message that action was needed promptly over the US economy.
In his first major news conference as president on Monday, Obama said the plan was "not perfect" but said it was essential to create new jobs and pull the US out of recession.
Republicans, and some moderate Democrats, have criticised the package, saying it contains too much unnecessary spending and too few tax cuts.
In the senate, at least 60 votes are needed to clear potential procedural hurdles and Democrats only control 58 seats.
"If it's more expensive, if it has wasteful spending added back in, then it would be very difficult for us to support," said Susan Collins, a Maine Republican senator who led the effort to forge a compromise with the Democrats, on Monday.
Obama had last week imposed a deadline of February 16 to sign the bill into law. However, it is not clear if this deadline will be met.
The US economy is in recession after months of financial turmoil following the subprime mortgage crisis, tight credit conditions, rising unemployment and global financial upheaval.