The CAP plan would eliminate deductions, close loopholes raise rates, implement new taxes, increase sales taxes, create new taxes... basically every form of a tax hike you can think of, all implemented on households with income above $250,000 per year.
What this gets, according to the Center for American Progress, is a tax system that barely raises Clinton-era levels of tax revenue, while the spending side of the ledger still projects to explode. CAP's plan gets tax revenue of 20.3% of GDP, below the Clinton years' high of 20.6% of GDP, with government spending projected to be significantly higher even under the most optimistic of situations. And by the 2030s, government spending is still projected to be over 25% of GDP in the most optimistic of scenarios. (You do not want to know what the pessimistic scenarios are. Something along the lines of an apocalypse.)
This is an unsustainable situation. It's government spending, not tax revenues, that needs the most attention. Even with very few policy changes, total tax revenues will rebound to above historical averages by the end of the decade. You can't soak-the-rich all the way to deficit reduction.
More honest progressives know that if they truly want to tax their way to a balanced budget, they need to tax the middle class and the poor. David Callahan writes that CAP's major mistake is exempting the non-rich from tax hikes, and that CAP "simply doesn't face up to revenue realities."
Medicare needs to be fixed. Social Security needs to be fixed. The old-age entitlement programs are what are projected to drive us down the road to Greece. Soaking the rich won't help that.