Congratulations, Louisiana voters. You’ve elected yourselves a Republican U.S. senator.

If that sounds like a shallow assessment of U.S. Rep. Bill Cassidy’s decisive win over three-term incumbent Mary Landrieu, chalk it up to the fact that Cassidy pursued a one-dimensional strategy of relentlessly linking Landrieu to unpopular President Barack Obama and his policies, with the Affordable Care Act at the top of the list.

Which is not to say it wasn’t a smart strategy. Clearly, it was an effective one.

Cassidy — as well as his future colleague David Vitter, who won his own Senate race four years ago by casting the vote as a referendum on Obama and played a major behind-the-scenes role in the Cassidy campaign — said what a majority of voters wanted to hear.

By the campaign’s last days, he’d said it so many times that, instead of repeating his contention that Landrieu supported Obama nearly all the time, he started using shorthand.

“And remember, Mary Landrieu, Barack Obama, 97 percent,” he said in a late campaign commercial.

Yet Cassidy, a smart and able man, didn’t talk much about himself or his own ideas. Nor did he delve into his history as a doctor in the charity system or what he hopes to do in the last four years of his six-year term, once he won’t have Obama to stand up to any more.

He debated three times but turned down additional invitations, claiming, nonsensically, that debates were simply scripted affairs. In the end, while Landrieu was trying desperately to shift the conversation from partisan politics to her own record and Cassidy’s character, he even left the campaign trail to cast votes in Washington.

The upshot is that many voters just don’t know him very well.

Much has been made about how this election marks the end of an era. As recently as a decade ago, most statewide elected officials were Democrats. Louisiana had already switched into the Republican column in presidential elections, but voters were still willing to split tickets. The last time Landrieu appeared on a ballot in 2008, she outperformed Obama by 12 percentage points.

But it’s also the beginning of a new period. Louisiana is finally, officially, a full-fledged member of the solid GOP South. And the distinction between state elections and national ones has nearly disappeared. How else to explain why some local Republican officials have voiced profound gratitude for Landrieu’s efforts to get the federal government to forgive disaster loans and keep flood insurance affordable, yet declined to back her in public? They have their own elections next year and don’t want to be tied to the president.

And as Louisiana politics have become nationalized, national politics have become more rigidly partisan. Consider the case of the U.S. Chamber of Commerce’s political arm. In the past, the group has backed Landrieu, and although it was actively involved in the Republican effort to take over the Senate, a top official there said it would do so again. But the endorsement never materialized, an apparent casualty of pressure to hold the party line.

By all appearances, Cassidy’s poised to vote the GOP line once he goes to the Senate. That’s what he said he’ll do, and that’s obviously what a majority of voters want.

What will be interesting to see is what happens when the state’s interests clash with Republican priorities. Landrieu undeniably delivered for Louisiana, whether that meant carving out a portion of offshore oil royalties and BP fines or landing hurricane aid. Cassidy says he’ll do the same, and hopefully that’s true. But given the GOP’s attitude toward spending, there may be situations where advocating for the state means bucking his own party.

There’s reason to believe he has it in him. Earlier this year, Cassidy joined Republicans from Louisiana, New York and other coastal states in passing a consumer-friendly flood insurance bill, even though they had to use a procedural maneuver to bypass a committee chairman who opposed putting the federal government more on the hook.

Cassidy has earned the right to chart his own path, of course. Still, there will be times when he’d be wise to follow in his vanquished opponent’s footsteps. I’m guessing that even the voters who threw her out wouldn’t mind.

Stephanie Grace can be contacted at sgrace@theadvocate.com. Read her blog at http://blogs.theadvocate.com/gracenotes. Follow her on Twitter, @stephgracenola.