The bill will extend coverage to 36m more Americans and provide affordable healthcare to 96%, supporters say.
If the bill passes, the next step will be to reconcile it with a separate Senate bill.
President Obama has made reform of the healthcare system a central plank of his domestic agenda.
‘Public option’
The House debate opened on Saturday with Democrats who support it saying it is needed morally, socially and economically.
HEALTHCARE IN THE US
47 million uninsured, 25 million under-insured
Healthcare costs represent 16% of GDP, almost twice OECD average
Q&A: US healthcare reform
Its mainly Republican opponents say the bill is over-ambitious, creates too much government control and could be hugely damaging to the economy.
The bill would allow the government to sell insurance in competition with private companies and make insurers offer cover to those with pre-existing conditions.
But this so-called "public option" has been scaled back in the wrangling that preceded the House vote.
Mr Obama was reportedly wooing wavering legislators by phone on Friday and scheduled personal meetings for Saturday morning.
White House spokesman Robert Gibbs said: "The sales pitch is simply that we’re on the cusp of the type of healthcare reform that this country has been talking about for decades.
"Do this for the country. Do this for your constituents."
‘Confident’
The Democrats have reportedly offered concessions to anti-abortion legislators to allow a vote on an amendment on whether to allow public funding for abortion programmes.
The Washington Post predicted the anti-abortion lobby would now win that amendment vote and anger abortion rights supporters within the Democratic Party.
House Democratic leader Steny Hoyer told MSNBC: "We’re confident we’re going to have the votes later today.
"There some disagreement on some issues but there’s universal commitment to passing a healthcare reform bill."
But Mississippi’
Although the House vote could come on Saturday, Mr Hoyer said it could be delayed to Sunday or even as late as Tuesday.
The New York Times said Mr Obama had secured 205 votes by Friday evening and was negotiating for the 13 more.
Once both the House and Senate have approved their own versions, a conference committee, made up of lawmakers from both houses, will convene to reconcile the two.
If both chambers then vote in favour of the reconciled version, it will be sent to Mr Obama for his approval, and become law.
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