"This is the best we can do given the Senate and the White House sentiment at this point in time, and it is at least a partial victory for the American people," she said. "I'll take that at this point."

The timing of the vote was crucial, as a new Congress is set to be sworn in Thursday.

Payroll taxes still set to go up

Despite the last-minute fiscal cliff agreements, Americans are still likely to see their paychecks shrink somewhat due to a separate battle over payroll taxes.

The government temporarily lowered the payroll tax rate in 2011 to 4.2% from 6.2% to put more money in the pockets of Americans -- but has cost about $120 billion each year. That tax cut expired Monday.

Americans earning $30,000 a year will take home $50 less per month. Those earning $113,700 will lose $189.50 a month.

The proposal laid out by the Senate and approved by the House does not address the sequester, a series of automatic cuts in federal spending. The bill just delays the sequester for two months.

So the deal adds another battle to this year's docket of congressional squabbles over money. The other two: the debt ceiling and a continuing budget resolution.

Obama said he hopes leaders in Washington this year will focus on "seeing if we can put a package like this together with a little bit less drama, a little less brinksmanship (and) not scare the heck out of folks quite as much."

He thanked bipartisan House and Senate leaders for finally reaching an resolution Tuesday, but said Congress' work this year is just beginning.

"I hope that everybody now gets at least a day off I guess, or a few days off, so that people can refresh themselves because we're going to have a lot of work to do in 2013."