President Obama on Tuesday dismissed the latest deficit-cutting proposal from Speaker John Boehner (R-Ohio) as "still out of balance."

"I think that we have the potential of getting a deal done, but it's going to require ... a balanced, responsible approach to deficit reduction that can help give businesses certainty and make sure the country grows," Obama told Bloomberg TV. "Unfortunately, the Speaker’s proposal is still out of balance."

Republicans on Monday countered the president's call for $1.6 trillion in tax increases with an offer to cut $2.2 trillion from the deficit with a combination of spending cuts, entitlement reforms and $800 billion in new tax revenue.

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Obama said the latest Republican plan, which would raise $800 billion in revenues without increasing the tax rates on the wealthiest Americans, "didn't add up."

"There's been a lot of talk that we can raise $800 billion or $1 trillion in revenues just by cutting loopholes," Obama said. "But a lot of your viewers understand that the only way to do that would be if you completely eliminated, for example, charitable deductions."

The president said "every hospital, university, and non-profit agency across the country would find themselves on the verge of collapse" under such a plan, and that realistically, only between $300 billion to $400 billion could be raised by eliminating deductions.

"If we're going to be serious about reducing our deficit while still being able to invest in things like education ... and if we're going to protect middle class, then we're going to have to have higher rates on the wealthiest Americans," Obama said.

Boehner shot back that Republicans are "willing to make concessions" in the talks, but need Obama to put forward a credible proposal.

"If the President really wants to avoid sending the economy over the fiscal cliff, he has done nothing to demonstrate it. Instead, he has offered a plan that could not pass either house of Congress," Boehner said in a statement.

"With our latest offer we have demonstrated there is a middle ground solution that can cut spending and bring in revenue without hurting American small businesses. The President now has an obligation to respond with a proposal that does the same.”

The fate of the Bush-era tax rates for the wealthy remains the central disagreement between the president and congressional Republicans in negotiations to avoid the "fiscal cliff." Obama has made tax hikes on the wealthy a precondition for any agreement, but Republican leaders have ruled out increasing the rates.

The White House on Tuesday threw another demand into the mix, saying an increase in the federal debt ceiling must be part of a final agreement.

"We're not going to negotiate on what is a fundamental responsibility of Congress," White House press secretary Jay Carney said, referring to the debt ceiling.

The Obama spokesman said the biggest obstacle in the fiscal talks is the refusal on the part of Republicans to acknowledge that tax rates for the wealthy need to go up.

"We need Congress to be serious about what the parameters of a deal look like," Carney said. "It's not good government for one party in Congress to refuse to acknowledge what a compromise must include."

But Carney refused to say whether Obama would accept a top tax rate of less than 39.6 percent — the level scheduled to take effect in January when the Bush tax rates expire.

Republican leaders have pressed Obama to "get serious" in their negotiations by putting entitlement reforms on the table. The president on Tuesday said he was "prepared to make some tough decisions" about entitlements, but balked when asked directly if that would include cuts to Social Security or Medicare benefits.

"I can't ask folks who are middle class, seniors who are on Medicare, young people who are trying to get student loans to go to college to sacrifice by not get anything from higher-income folks," Obama said.

Pressed on the issue, Obama said he was "happy to look at how we can actually make those entitlement programs stronger" but avoided taking a definitive stance on whether benefits could change.

The president said he did not believe that negotiators were going to be able to come up with comprehensive entitlement or tax reform packages in the next two weeks, urging instead a "down payment" that would avert the fiscal cliff but allow more time to craft the eventual program.

"What I've suggested is, let's essentially put a down payment," Obama said. "On taxes, let's let tax rates on the wealthiest go up ... and then let's set up a process with a time certain at the end of 2013 or the fall of 2013 where we work on tax reform, we look at what tax loopholes and deductions both Republicans and Democrats agree we can close, and it's possible we can lower rates by broadening the base at that point."

— Amie Parnes contributed.

This story was updated at 2:08 p.m.