In remarks after the Senate vote, Obama said that while congressional passage of the compromise measure averted a default that would have "devastated" the nation's economy, and that the measure "is an important first step to ensuring that as a nation we live within our means," it also "allows us to make key investments in education and research that will lead to new jobs and assures we are not cutting too abruptly while the economy is still fragile."

But, Obama continued, the compromise measure requires a "next step" in which both sides of Congress must come up with a "larger plan to cut the deficit, which is important to the long-term health" of the nation's economy. "Since you can't close the deficit with just spending cuts, we'll need a balanced approach, where everything is on the table," he said.

That means, he continued, "making some adjustments to protecting health programs like Medicare so they are there for future generations," and it also means "reforming the tax code so that wealthy Americans and big corporations pay their fair share." The nation, he said, "can't balance the budget on the backs of the very people who have borne the brunt of this recession."

"Everyone"—including the wealthy and corporations—is going to have to "chip in" to help reduce the deficit, Obama said, "and that's the principle that I'm going to fight for" during the next step in the deficit reduction process.

AARP, the powerful lobbying group for retired Americans, said in a statement after the Senate vote that while it was "gratified" that the compromise package "did not cut Social Security, Medicare and long-term care in the first round" of the plan, and that the group is "pleased" all of these benefits are protected if the "so-called 'super committee' fails to reach an agreement later this fall," AARP will "remain vigilant in our efforts to protect the health and retirement security of seniors and future retirees."

In the Senate vote on Tuesday, 28 Republicans, 45 Democrats and one Independent voted in favor of the proposal, while 19 Republicans, six Democrats, and one Independent voted against the agreement.

Sen. Richard Shelby, R-Ala., ranking member on the Senate Banking Committee, was one of the 19 voting against the measure. In a statement after the vote, Shelby said that the package "compromises our financial future," and that its "sole immediate guarantee is that the debt ceiling will increase."

The plan's spending cuts, Shelby said, "are illusory because they are spread out over a decade and subject to override by future Congresses." Even if all of the legislation's "promises become reality–and that's a huge if–the debt will still increase by approximately $8 trillion over the next ten years," he said.

The goal, Shelby continued, "should have been to avoid a downgrade of our creditworthiness by enacting meaningful spending cuts. We may still fail to achieve the former because we did not summon the courage to accomplish the latter."