Stephanie Grace: Is Gov. Bobby Jindal a ­politician or a pundit?

It’s been a jam-packed and grueling legislative session, but Gov. Bobby Jindal has apparently managed to take a break from the big fights in Baton Rouge to think some big thoughts about Washington.

Never mind the raging debate over just how much the state should spend — and on what. And forget Jindal’s own troubles, from the Louisiana Supreme Court’s quibbles with his education reform package, to his failure to get a hearing on whether to scrap the state income tax, to the investigation involving his former top health aide, to the worst poll numbers of his career.

Instead, readers who visited CNN’s website over the long Memorial Day weekend might well have concluded that Jindal is singularly focused not on his own woes, but on President Barack Obama’s. All those “scandals” in Washington, from the IRS scrutiny of tea party groups that applied for tax-exempt status to the mess over Benghazi, he asserted in an opinion piece, “flow out of big government philosophy.”

This is hardly the first time that the governor has spoken out on matters well outside his gubernatorial portfolio. Politician Jindal has been keeping busy at home, but so has pundit Jindal, who rarely passes on an opportunity to weigh in.

Not that politician Jindal and pundit Jindal are two entirely different characters. At the least, both appear to be working out of the same playbook, with the same goal in mind: to get noticed, on a potentially presidential level.

There have been speeches and network talk show appearances, some in his role as head of the Republican Governors Association, and some just because, despite his relative youth, Jindal’s now one of the more seasoned GOP governors on the circuit. And there have been columns, not only in local papers but for out-of-town outlets.

Sometimes Jindal marks his ideological territory by focusing on a state-level issue, like when he defended his refusal to expand Medicaid for Louisianians in the pages of the Washington Post. Sometimes he simply offers advice on how Republicans should position themselves for electoral success.

He’s been known to use these platforms to say something new and intriguing. That’s what happened when Jindal took to the Wall Street Journal’s opinion page in December to suggest that oral contraceptives, the focus of a huge partisan fight over government-mandated prescription coverage, should just be sold over the counter — in part, he said, because Republicans were losing women on this issue. The proposal never gained traction, and he quickly jumped to the next topic.

More often, Jindal takes predictable positions and tries to stand out by expressing them more forcefully, more quotably, or both. His most-successful effort of this sort followed the presidential election, when he was one of the first prominent Romney backers to distance himself from the failed campaign, and when he famously called on fellow Republicans to soften their harsh rhetoric and stop being the “stupid party.”

Back in Baton Rouge, some of Jindal’s second-term policy pushes seem designed with the same purpose in mind. Last year’s huge education reform package, most of which survives despite the unfavorable Supreme Court rulings, positions Jindal as a point person in a national drive. His income tax elimination, had it passed, would have accomplished a similar goal.

Now, the aborted effort might end up serving a different function, as a test case of just how damaging Jindal’s troubles back home are to the party leader image he’s been so obsessively crafting.

Banishing the state income tax was supposed to be a triumph, at least among the anti-tax true believers who hold so much sway in the national GOP. But does his spectacular failure to sell the idea — and to convince pretty much anyone at all that Louisiana should raise sales taxes to replace the lost revenue — turn the episode into a tragedy? Or will the outside world view it more as a footnote than an embarrassing failure?

If nothing else, Jindal’s latest column on suggested that he’s eager to find surer political ground.

So did an email to journalists making sure they’d seen the post; it came, tellingly, from Jindal’s Alexandria, Va., consulting firm, OnMessage Inc.

OnMessage has vast experience in national GOP campaigns, and in shaping the governor’s image. Its partners include Timmy Teepell, Jindal’s former chief of staff and political right-hand man, and Curt Anderson, who lists himself as a co-author of the governor’s 2010 book, “Leadership and Crisis.”

When it comes to their client’s approach, the advisers are actually aptly named. Jindal may be jumping from topic to topic, but he is indeed staying “on message.” That message? That he just wants to be the messenger.

Stephanie Grace can be contacted