Obama welcomed the result of the vote but cautioned against an early celebration.
"Now is not the time to pat ourselves on the back - now is the time to dig in and work harder," he said.
"In this final phase we should engage with each other with civility and seriousness that has brought us this far and that this subject deserves."
The healthcare package aims to reduce costs, regulate the insurance market and provide greater access to healthcare to millions of uninsured Americans.
The plan that was voted on by the senate finance committee will be combined with the US senate health panel's own package.
The full senate is set to debate the merged package in the next few weeks.
Max Baucus, the Democratic chairman of the panel, said while opening the committee meeting: "Pretty much everything has been said and now it's time to get the job done.
"Americans are looking for common-sense solutions."
Obama has made reform of US healthcare the centrepiece of his domestic policy agenda, but his plans have faced stern Republican opposition.
They say that the plans recommended by senior Democrats are too expensive in the wake of a $768bn bailout of US financial institutions, and that they mark interference into the private healthcare sector.
Senator Charles Grassley, the senior Republican on the panel, said: "We can now see clearly that the bill continues its march leftward.
"This bill is already moving on a slippery slope to more government control of healthcare."
But Snowe's support of the senate finance committee's package could help the Democrats towards the 60 senate votes needed to head off procedural obstacles.
"Americans want us to craft a package that will get the 60 votes to pass," said Baucus, who led months of negotiations with three committee Republicans, including Snowe.
Non-partisan analysts estimated last week that the package under consideration by the senate finance committee would cost $829bn - well short of Obama's target of $900bn.