New York Times columnist David Brooks may be a (sorta kinda) conservative. But by all accounts, he also has the ear of President Obama. And in his column today, Brooks — trying to imagine some big initiatives that the president might push as he prepares to accept his party’s nomination for a second term — offers Obama a bold idea: put climate change at the top of his policy agenda.

President Obama has occasionally said he’d like to do something about climate change if he gets a second term. Given the country’s immediate economic and fiscal problems, this seems obtuse to me. But if this is really where Obama’s passion lies, he should go for it.

He could vow to double down on green energy and green technology. He could revive cap-and-trade legislation that would create incentives for clean innovation. He could propose a tax reform package that would substitute gasoline and energy consumption taxes for a piece of our current income taxes. He could say that his No. 1 international priority will be to get a global warming treaty ratified by all the major nations.

This would be a big, intellectually serious agenda, designed to address a big problem.

Well, yes, it would be that, wouldn’t it?

On the other hand, we are coming off a Republican National Convention in which the one significant mention of the climate issue was a laugh-line delivered by the party’s nominee. Mitt Romney’s voice dripped with sarcasm at the idea that any U.S. president would put an ounce of effort into stemming the rise of the oceans, or any other mitigation of the harms caused by climate change, instead of “helping you and your family” — as if the two aims were in implacable conflict.

So when a right-leaning columnist comes along to suggest that a Democratic president put climate at the center of his agenda, I put my cheer reflex on pause and scratch my head.

Brooks’ proposition leaves me with two questions:

First, is Brooks for real here, or does the suggestion just play into the GOP’s hand? If Obama actually followed Brooks’ advice and picked up the climate banner, wouldn’t Romney just load up the wisecracks and make hay with his base?

Second, and more interestingly, should Obama run with Brooks’ idea anyway? Let Romney sneer! We’re in a hellacious weather cycle, with record temperatures, droughts, and storms that have focused the public mind. What if the president faced the nation on Thursday as he accepts the Democratic nomination and said, we’re going to deal with the climate precisely because that will help you and your family?

I don’t know whether the American electorate would embrace that message today, and I’m not betting the president will choose this path — it looks risky in the swing-state-voter game by which this election is likely to be won. Still, it’s a tantalizing scenario to play out.

What do you think: Should Obama go all in on climate? How would that affect the election? And would it bring the U.S. any closer to averting the global mess we’re barreling toward?