Steny Hoyer, the House Democratic leader, told NBC television's Meet the Press programme that a handful of party members were still to commit to the bill.
"There are still members looking at it and trying to make up their minds," he said.
But Hoyer said that the holdouts were "in the low single digits" and that he also expected the bill to get "216-plus votes when we call the roll".
Obama has staked his own credibility on the bill which would provide health insurance coverage to 95 per cent of Americans, extending current coverage by 32 million people.
He put forward the current proposal for reformsin an attempt to get the bill passed after months of deadlock over the issue.
On Saturday, Obama campaigned at a meeting in of Democrats in Washington DC for them to vote for the bill.
The bill has narrowly passed votes in both the House of Representatives and the senate, but a reformed bill now has to pass Sunday's vote and a later ballot in the senate.
There are a series of votes on Sunday in the House of Representatives. First on the "rule" to govern the debate, then a package of "fixes" to the senate's version of the bill, and then the senate bill itself.
"We want to make it absolutely clear that we're modifying the senate bill," Chris Van Hollen, a Democratic representative, told reporters on Sunday.
According to the latest Gallup poll, only 45 per cent of Americans support the healthcare plans.
There has been strong opposition to the changes, with opponents stating that they amount to government overreach and would be too costly.
"The American people don't want this to pass. The Republicans don't want this to pass. There will be no Republican votes for this bill," Eric Cantor, the House's second-ranking Republican, told ABC News on Sunday.
Democrats argue that an estimate by the non-partisan Congressional Budget Office (CBO) that said that the reforms could cut $130bn from Washington's huge budget deficit by 2019 and $1.2 trillion by 2029.
The CBO estimated that the bill would cost $940bn over the next ten years.
Al Jazeera's Rosiland Jordan, in Washington DC, said that Obama is facing tough opposition: "The Republicans have been able to get many people in the so-called tea party movement to come out to Capitol Hill this weekend.
"In fact, some of them have been able to come inside a congressional office building to try to meet those members of congress who they think might vote for the measure and to try to make a last-ditch effort to persuade them to vote against this measure."
Jordan said that the bill would prevent insurance companies denying coverage to people based on the medical history.
"The real benefits of this programme are going to take about four years or so to be put into practice. So this is not an automatic extension of health coverage. Certainly not the kind we would see in industrialised Europe."
If the measure clears the House vote, the US senate would begin looking at the changes to the bill next week.