Obama also acknowledged that many fellow Democrats aren't happy about what he negotiated with the Republicans.
He pressed for passage by the end of the year as he told lawmakers in his radio and Internet address Saturday that "our recovery will be strengthened or weakened based on the choice that now rests with Congress."
The deal would extend for all earners cuts in income tax rates that are set to expire next month. It would renew jobless benefits for the long-term unemployed and trim Social Security taxes for one year.
Republicans support the plan because it would not impose higher taxes on the wealthiest, as Obama long had wanted to do. Democrats object to the pact on grounds that it is too generous to the rich.
Obama said that the deal will require that both Democrats and Republicans accept some items they do not like. However, he also said the agreement will help the middle-class families that should be spared further economic hardship.
The Senate is expected to vote on the tax package on Monday.
With just days to go before the holiday recess, the house has still not scheduled a vote.
The Associated Press contributed to this report.