Stop the presses. Republicans and Democrats are on the verge of figuring out that the solution to the budgetary mess they have created requires talking. To each other.

That appears to be what happened last week, as President Obama circumvented the Senate Republican leadership to meet over dinner – personally paid by Obama – with 12 senators, including his former election opponent, Sen. John McCain, R-Ariz. They should try the same approach with the 2010 health care reform law that needs reforming.

Last week’s meeting appears, at least initially, to have been worth the effort. McCain and Sen. Tom Coburn, R-Okla., gave thumbs-up signs after the meal, while Sen. Mike Johanns, R-Neb., was flat-out optimistic. “I think what he is really trying to do is just start a discussion and break the ice, and that was appreciated,” he said. “His goal is ours – we want to stop careening from crisis to crisis and solving every problem by meeting a crisis deadline.”

Part of the key to these talks was for Obama to ensure that rank-and-file Republicans understood what he was proposing: $900 billion in cuts – including entitlement programs that have been exempted from the sequester – in exchange for $600 billion in new revenue by changing the tax code. One senator, speaking to NBC’s First Read, reported that he learned for the first time of the cuts that Obama was willing to make. Republican leadership hadn’t shared that information before.

Meanwhile, Republicans are (again) putting forward a plan to repeal the Affordable Care Act, but this time they are also proposing to replace it. Their ideas are welcome, but they are coming late to the dance.

They should have been seeking to influence the shape of the law when it was debated three years ago instead of simply trying to block it. Health care reform was, and remains, an urgent matter in a country that spends far more on health care than any other developed nation and for results that are only average. The best time to have engaged in the process was when the law was being drawn up, not after it was debated, signed and endorsed by the U.S. Supreme Court.

Yet, the plan that Obama and congressional Democrats came up with did too little to control the rising costs of health care, even as they expanded the number of Americans covered and made other important changes. Without controlling costs, though, everything else will be moot.

Republicans should follow Obama’s lead and open a serious dialogue about how to improve the health care law. If all they do is introduce a repeal that cannot become law and propose changes that will never be adopted, then Americans will know this is nothing more than politics as usual.

But if they show a willingness to engage on a subject that still requires attention, they might yet serve Americans well on health care. It’s late, but maybe not too late.