Obama is set to sign the bill as soon as Congress can ship it to him. The Senate broke through months of stalemate in by a 59-39 vote. The House planned to vote around midday on Thursday.
At issue are jobless payments averaging $309 a week for almost 5 million people whose 26 weeks of state benefits have run out. Those people are enrolled in a federally financed program providing up to 73 additional weeks of unemployment benefits.
Under best-case scenarios, unemployed people who have been denied jobless benefits because of the partisan Senate standoff can expect retroactive payments as early as next week in some states.
Democrats have become more aggressive in attacking the Republican Party for opposing the measure, which has been stripped down so that it's essentially limited to a $34 billion, six-month renewal of unemployment insurance for the chronically jobless.
Obama promised to sign the measure quickly once the House acts and denounced the "weeks of parliamentary roadblocks by a partisan minority" that had stalled approval in the Senate.
"Americans who are working day and night to get back on their feet and support their families in these tough economic times deserve more than obstruction and partisan game-playing," Obama said in a statement Wednesday night.
Republicans say they support the benefits extension but insist any benefits be financed by cuts to programs elsewhere in the $3.7 trillion federal budget. Republican moderates Olympia Snowe and Susan Collins were the only Republicans to support the bill Wednesday.
Sen. Ben Nelson of Nebraska was the only Democrat to break with his party to oppose the bill.
Democrats tout the economy-boosting effect of unemployment checks since most beneficiaries spend them immediately, and they say paying for them with cuts to other programs dilutes the stimulative effect.
Economists say the measure will probably have a modest beneficial effect on the economy. It represents less than one-quarter of 1 percent of the size of the $14.6 trillion economy, and is far smaller than last year's $862 billion stimulus legislation.