The White House insists the next debt deal must have just as much tax revenue as spending cuts. President Obama hasn't specified exactly what he will demand in the next round of negotiations, but budget experts like Chuck Marr of the Center on Budget and Policy Priorities predict that "the most live option" would be a proposal that Obama had included in his original 2013 budget: limiting the tax write-offs for the wealthiest taxpayers, usually referred to as a "28 percent cap." But even it passed, it wouldn't be enough to revenue to meet the White House's likely target for tax savings.

(Ray Stubblebine-AP) (Ray Stubblebine-AP)

Under Obama's original budget proposal, the wealthiest 2 percent of Americans would take two kinds of tax hits: In addition to seeing their tax rates rise on income above $250,000, the wealthiest taxpayers would only be able to reduce their tax liability by 28 percent of the value of certain tax deductions and exemptions. (Currently, the top tax brackets are allow to use a higher percentage of tax write-offs.) It's a way to limit tax breaks without eliminating specific deductions or exclusions; a Mitt Romney-style dollar limit would be another one. 

If Obama had completely gotten his way on taxes in the first round of the debate—applying his preferred Bush tax cuts and a 28 percent deduction cap to those with income above $250,000—the change would have raised about $520 billion through 2022, according to Marc Goldwein of the Center for a Responsible Federal Budget. If it started in 2014, it would raise closer to $480 billion through 2022.

But the Jan 1 "fiscal cliff" deal set the cut-off for the Bush tax cuts at $450,000, instead of $250,000, lowering people's rates further. As a result, Goldwein very roughly estimates Obama's deduction cap would raise in the broad range of $400 billion through 2022. If that's the case, it probably wouldn't be enough to offset the $1.2 trillion "sequester" according to the White House's demand of 1:1 spending cuts to revenue. You would also be hitting the same group of Americans whose taxes went up because of the first fiscal cliff deal, which could be another political challenge. And if you applied Obama's 28 percent deduction cap only those taxpayers above $450,000 threshold—who make up just 0.7 percent of all taxpayers—you'd raise "a lot less money" than $400 billion," Goldwein concludes.

That said, there was a small part of the Jan 1 deal that indicated that the White House might try to raise taxes on a broader swath of the population in the second round of negotiations. It actually included some smaller limitations on deductions and exclusions for taxpayers at the $250,000 individual/$300,000 family threshold—reimposing the PEP and Pease limits that the Bush tax cuts had suspended for more than a decade. That could help the administration make the case that Congress should be willing to eliminate tax deductions and exclusions starting at the $250,000/$300,000 level, given that legislators already passed something similar in January.  

But whether Obama's deduction cap can raise $400 billion or less, it will be all the same to Congressional Republicans who believe that revenue should be off the table entirely. Even Sen. Bob Corker (R-Tenn.), who proposed a $50,000 deduction cap as part of a fiscal cliff solution last year, believe that the focus should be first and foremost on entitlements. "Sen. Corker believes passing fundamental entitlement reform is the most important action we can take in ensuring our country's solvency and hopes that will be the primary focus of discussions and actions this quarter," said his spokeswoman Laura Herzog.