Read the study here. Here's a summary of Brookings' key findings:
Our major conclusion is that a revenue-neutral individual income tax change that incorporates the features Governor Romney has proposed -- including reducing marginal tax rates substantially, eliminating the individual alternative minimum tax (AMT) and maintaining all tax breaks for saving and investment -– would provide large tax cuts to high-income households, and increase the tax burdens on middle- and/or lower-income taxpayers. This is true even when we bias our assumptions about which and whose tax expenditures are reduced to make the resulting tax system as progressive as possible. For instance, even when we assume that tax breaks -– like the charitable deduction, mortgage interest deduction, and the exclusion for health insurance -– are completely eliminated for higher-income households first, and only then reduced as necessary for other households to achieve overall revenue-neutrality– the net effect of the plan would be a tax cut for high-income households coupled with a tax increase for middle-income households.
Brookings is quick to point out that it did not "score Governor Romney’s plan directly, as certain components of his plan are not specified in sufficient detail, nor do we make assumptions regarding what those components might be." But it did say that Romney's plan would lower the tax burden on the rich and increase it on all other taxpayers even after making all reasonable assumptions in favor of progressivity.
The Washington Post's article on the Brookings' analysis puts it this way:
The study was conducted by researchers at the Brookings Institution and the nonpartisan Tax Policy Center, who seem to bend over backward to be fair to the Republican presidential candidate. To cover the cost of his plan — which would reduce tax rates by 20 percent, repeal the estate tax and eliminate taxes on investment income for middle-class taxpayers — the researchers assume that Romney would go after breaks for the richest taxpayers first.