Obama also said the widening income inequality and the lingering effects of the financial crisis have frayed America's social fabric and undermined Americans' belief in opportunity.
"I will seize any opportunity I can find to work with Congress to strengthen the middle class, improve their prospects, improve their security," he said.
Obama, 51, now in the seventh month of his second innings at the White House, he vowed not to be cowed by his Republican adversaries in Congress and said he was willing to stretch the limits of his powers to change the direction of the debate in Washington.
Speaking a few days after the acquittal in the Trayvon Martin case prompted him to speak about being a black man in America, Obama said the country's struggle over race would not be eased until the political process in Washington began addressing the fear of many people that financial stability is unattainable.
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"Racial tensions won't get better; they may get worse, because people will feel as if they've got to compete with some other group to get scraps from a shrinking pot," he said.
Upward mobility, "was part and parcel of who we were as Americans. And that's what's been eroding over the last 20, 30 years, well before the financial crisis," Obama said.
"If we don't do anything, then growth will be slower than it should be. Unemployment will not go down as fast as it should. Income inequality will continue to rise," he said, underlining that "that's not a future that we should accept."
The US economy is "far stronger" than four years ago, he said, yet many people who write to him still do not feel secure about their future, even as their current situation recovers.