This is going to be a column that praises President Obama’s new charm offensive with congressional Republicans and suggests some useful background reading for the next get-together. First, though, I’ve got to get a bit of snark out of the way.

Such as: Isn’t this the same Obama who decreed that playing nice with Washington wasn’t working, so he’d be taking his case straight to The People? It’s a false choice between the two approaches, but this tactical switcheroo is rather dizzying.

And, excuse me, if the White House thinks it’s worth the try, couldn’t Obama have attempted this a few months ago, before the “sequester” kicked in?

Still, let’s look ahead. It is hard to imagine a breakthrough without intensive presidential involvement, which makes the new outreach so welcome. I know Republican senators, prospective members of Obama’s common-sense caucus, who have waited in vain over the past few years for a call from the White House chief of staff, never mind the president himself.

Meanwhile, there are a few signs of thaw on the Republican side, indications that Obama’s mealtime diplomacy may not be futile. Specifically, several Republican senators — Arizona’s John McCain, South Carolina’s Lindsey Graham, New Hampshire’s Kelly Ayotte — have dared to say that they would, gasp!, consider raising revenue.

The senators attach two caveats: Revenue must come through fundamental tax reform (getting rid of loopholes, not raising rates) and be accompanied by reined in entitlement spending.

In theory, both sides agree on these approaches. In practice, the entitlement debate in particular has become mired in unnecessary partisan line-drawing. One side deems as essential proposals that the other has declared anathema. Two prime examples: turning Medicare into a premium support (scary version, “voucher”) program and raising the Medicare eligibility age. Endlessly arguing over those is not likely to accomplish anything in the current environment.

Hence this suggested reading: a new report from the Brookings Institution’s Hamilton Project, “15 Ways to Rethink the Federal Budget.” Granted, the Hamilton Project is associated with Democratic policymakers, albeit centrist ones such as co-founder Robert Rubin; its animating vision of government is not the same as, say, Paul Ryan’s. So proposals such as a carbon tax or value-added tax, however sensible, aren’t likely to fly.

But the report contains several ideas that even Ryan could love — or, at the very least, that the House Budget Committee chairman should not reject out of hand. For example, where Ryan proposes giving Medicare beneficiaries a set amount with which to obtain insurance, Michael Chernew of Harvard Medical School and Dana Goldman of the University of Southern California propose giving Medicare providers a set amount to cover beneficiaries.

This “global payment” would replace the perverse incentives of the current fee-for-service system — to bill for as many procedures and services as possible — with a spur toward efficient, comprehensive care. This approach exists currently, in the form of the private Medicare Advantage programs that serve about a quarter of beneficiaries (and that, notably, have been a darling of Republicans) and in accountable care organizations being established under Obamacare. Estimated savings: $100 billion over 10 years.

Another idea, from MIT’s Jonathan Gruber, would attack Medicare costs from the consumer side. It would deal with the current risk of catastrophic costs by adding an out-of-pocket maximum tied to beneficiaries’ incomes so that poorer seniors would face less risk.

But it would also heavily tax seniors’ supplemental insurance plans that fail to impose adequate cost-sharing on beneficiaries. Again, this proposal could appeal to both sides: The Obama administration has suggested limiting Medigap policies, and the Ryan approach is all about giving consumers incentive to control costs. Estimated savings: $125 billion over 10 years.

On the tax side, Alan Viard of the American Enterprise Institute proposes replacing the home mortgage interest deduction with a tax credit worth 15 percent of annual interest on the first $300,000 of a mortgage — spreading the tax benefits of homeownership more fairly and avoiding subsidizing ever-bigger homes. Estimated savings: $300 billion over 10 years.

Karen Dynan of Brookings proposes changing tax incentives to encourage low- and moderate-income households to save more for retirement and education, while reducing the subsidies for wealthier taxpayers. Estimated savings: $40 billion over 10 years.

The two sides are talking. That’s good. Before the next meal, they might take a look at the Hamilton report. It could help the conversation move beyond “no new taxes” and “please pass the salt.”

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