In the video, Obama says he will seek to lower deficits in a "responsible way" and make government "leaner and smarter," but without undermining the vital role Democrats believe the government must play in the economic recovery. Obama wants to spend more on education, research and development, and the nation's infrastructure - areas that many Republicans view as ripe for deep cuts.
"My number one focus is going to be making sure that we are competitive, that we are growing, and we are creating jobs not just now but well into the future," Obama said in his message to members of Organizing for America, his grass-roots organization.
McConnell said on "Fox News Sunday" that new spending defies the message sent by voters in November, when Republicans took control of the House and gained six seats in the Senate.
"We'll take a look at his recommendations," McConnell said. "But this is not a time to be looking at pumping up government spending in very many areas."
On the same show, Sen. Richard J. Durbin (D-Ill.) said spending cuts could halt the recovery, a view shared by the president's bipartisan deficit commission.
"They said be careful," said Durbin, a member of the commission. "Don't start the serious spending cuts until we're clearly out of the recession in 2013. Maybe it will be sooner. But that warning is something we shouldn't forget."
In an appearance on NBC's "Meet the Press," House Majority Leader Eric Cantor (R-Va.) said leaders in his chamber plan to immediately pursue the deep cuts they promised in last fall's campaign. Cantor added that cuts to the Pentagon's budget will also be considered, a step many Republicans normally have been unwilling to take.
"Every dollar should be on the table," he said.
The effort in the House will begin Monday, when Republicans will consider a resolution that would enact immediate and drastic spending cuts to domestic programs of nearly every variety.
The resolution was designedto give Republicans a platformon spending to contrast with Obama's State of the Union message. But many conservative Republicans felt it didn't go far enough and amended the measure to require tougher cuts than leadership intended, highlighting a fissure within the GOP that could make it even harder for the parties to find common ground.
A chance of compromise
The first big test of how the new dynamics in Washington will play out is likely to come in late spring, when lawmakers must agree on a funding resolution to keep the government operating.
Several weeks after that, they must decide whether they are willing to raise the nation's debt limit, a normally pro forma action that allows the government to meet its obligations. This year, however, many conservatives have signaled that they are unwilling to extend federal borrowing power beyond its current limit, and Cantor said Sunday that Republicans will use the vote as leverage against Democrats.