"I'm willing to eliminate whatever we can honestly afford to do without," he said. "But let's make sure that we're not doing it on the backs of our most vulnerable citizens."
Senate Republicans, meanwhile, said they're none too impressed with the president's plan to propose a budget freeze.
"I would remind you that in the speech last year there was a recommendation for a three-year freeze," the Senate's top Republican, Mitch McConnell of Kentucky, said. "And the problem with that is it freezes in place an extraordinary increase in spending that's occurred over the last two years. So it strikes most of us that the effort by the House of Representatives to get us back to 2008 spending levels would be the direction to go if we really wanted to have an impact on our annual deficit problem."
Obama seemed willing to renegotiate portions of his signature legislative achievement -- the health care reform bill that he signed into law last March.
"Now, I've heard rumors that a few of you have some concerns about the new health care law. So let me be the first to say that anything can be improved," he said. "If you have ideas about how to improve this law by making care better or more affordable, I am eager to work with you."
The House of Representatives, led by a new Republican majority, voted last week to repeal the health care law, but the movement will almost undoubtedly die in the Democratically-controlled Senate.
House Republicans and some conservative Democrats have vowed to re-examine portions of the law to try and repeal specific items, while letting some of its provisions stand.
"We can start right now by correcting a flaw in the legislation that has placed an unnecessary bookkeeping burden on small businesses," the president said. "Instead of re-fighting the battles of the last two years, let's fix what needs fixing and move forward."
Most of the speech was focused on domestic issues -- the president did not even mention foreign policy until nearly an hour into the speech.
Obama gave his administration credit for the nation's progress on the world stage over the last two years, including the new START treaty and progress in Iraq and Afghanistan.
"America's moral example must always shine for all who yearn for freedom, justice, and dignity," he said. "And because we have begun this work, tonight we can say that American leadership has been renewed and America's standing has been restored."
Obama announced he will travel to South America in March, his first trip there as president. He will make stops in Brazil, Chile and El Salvador.
The White House had said that what the president outlined Tuesday is a "robust agenda" -- and a message that both Democrats and Republicans can support.
"He's going to be proposing strategic, targeted spending that's smart," White House senior advisor Valerie Jarrett said on "Good Morning America." "We want to invest in education. We want to invest in infrastructure. But we also have to tighten our belts and be more efficient."
But Republicans said that "investment" is just a code word for more government spending, which they say they were elected to rein in.
"I'm hopeful that the word investment isn't just more stimulus spending and bigger government here in Washington," House Speaker John Boehner said.
"If history is our guide, most Republicans will agree with 80 percent of what he says, but disagree with 80 percent of what he does," Rep. Jeb Hensarling, R-Texas, said this morning.