President Barack Obama launched what some call a “charm offensive” last week by picking up the tab for a dinner with 12 Republican senators — including our own Lindsey Graham — at a fancy Washington restaurant.

Yet while that’s a generous gesture, it offers no guarantee that the president and Congress will finally figure out how to cover the soaring federal-budget bill that they persist in running up by spending far beyond our means.

And with yet another fiscal deadline looming, passing the steak sauce is much easier than reaching across the aisle for overdue spending restraint.

Congress must pass, and the president must sign, a continuing resolution by March 27 to avert a federal-government shutdown.

Sound familiarly ominous?

In just the last 10 weeks or so, our political class has taken us to the brink of the fiscal cliff, boosted the ever-ascending debt ceiling and forced sequestered spending cuts.

But perhaps those failures of leadership have at last shamed Congress — and the president — into positive, overdue action.

After last Wednesday’s night out with the president, Sen. Graham called the occasion “productive and substantive.” He expressed hope that “it will serve as the beginning of a new, long-overdue paradigm where people in elected office actually begin talking to each other about meaningful issues.”

Certainly on the long list of “meaningful issues” facing our nation, none is more pressing than the alarming gap between Washington’s revenues and expenditures: As of Monday, the national debt was a record $16.72 trillion — and still climbing.

So it’s encouraging to know that President Obama will seek budgetary compromise this week in meetings with lawmakers from both parties on Capitol Hill.

Of course, that scenario would be much more reassuring if the president and other prominent Democrats had not for so long — and so ludicrously — denied that Washington’s bottom-line mess is essentially a spending problem.

And it’s far past time for the president and his party to recognize that without comprehensive entitlement reform, the federal budget is bound for a demographically driven train wreck.

On the brighter side, Sen. Tom Coburn, R-Okla., who has earned a solid reputation as a fiscal hawk, detects some movement toward entitlement reality by the White House. Sen. Coburn said Sunday on NBC’s “Meet the Press”:

“I think a great sign is that the president is now talking privately about Medicare and the crisis that we face in Medicare.”

Sen. Coburn added of Mr. Obama: “Go back and see what he said in 2006, 2007, 2008. When he said Medicare was the real crisis, Social Security was the real crisis. He said we were stealing from future generations.”

President Obama was right about those entitlement dangers back then. Too bad he has been wrong since then in resisting the hard choices needed for Medicare and Social Security — and the pleas on that front from his own debt commission.

As for the president’s continued fixation for raising taxes on the rich, most of the $600 billion hike in the fiscal-cliff agreement that Congress passed at the start of the year falls on the wealthy.

That doesn’t mean Republicans should reflexively reject practical ideas about “enhancing” revenues by closing some tax loopholes.

Then again, that also doesn’t mean we can tax our way back to financial balance.

Last week the Congressional Budget Office projected that federal tax revenues will reach a record high this year. It was another reminder that the spending side of the equation is the crux of the debt crisis.

And while it’s nice to know that after four straight trillion-dollar-plus deficits we’re on track for a shortfall of a mere $845 billion this year, that’s still nearly double the annual red-ink record before Mr. Obama became president.

So good for President Obama in trying to find common ground on the budget.

But he should know by now that treating Republican senators to free dinners can’t void this indisputable maxim from the late, great Milton Friedman:

“There’s no such thing as a free lunch.”