You’ve surely heard the one about how all politics is local, the rule of thumb popularized by the late U.S. House Speaker Tip O’Neill.

After watching this year’s endless elections, I’m wondering whether the saying has outlived its usefulness.

Consider the U.S. Senate election. The contest between Republican U.S. Rep. Bill Cassidy and Democratic incumbent Mary Landrieu played out as something of a referendum on the premise. Cassidy’s focus on President Barack Obama easily trumped Landrieu’s record on localized issues, including billions of dollars in disaster aid and a landmark law to siphon some offshore oil royalties into state coffers. You could call it the triumph of partisanship over pork.

Same goes for the two contested U.S. House elections, at least once the crowded primaries transitioned into Republican-versus-Democrat runoffs. From that point on, there was no question that two first-time GOP candidates, Garret Graves and Ralph Abraham, would defeat their seasoned Democratic opponents, colorful and controversial ex-Gov. Edwin Edwards and Monroe Mayor Jamie Mayo. All anyone had to do was look at the 5th and 6th districts’ leanings on big philosophical issues to see a pair of blowouts in the making.

Even some local races carried the distinct tinge of national debates.

In explaining why Landrieu had to fight harder than ever for the support of the state sheriff’s association, Jefferson Parish Sheriff Newell Normand said during the campaign that many members were thinking about their own re-election battles next year (Normand, a Republican, admitted that he, too, considered his future prospects in declining to endorse Landrieu, as he’d done six years earlier, despite his gratitude for Landrieu’s efforts on the department’s behalf after Hurricane Katrina). Obama’s face was a regular feature of attacks by and on behalf of Cassidy, and other politicians, it seems, don’t want the same thing to happen to them.

That’s not an idle concern. It actually happened in the heated race for the Public Service Commission’s 1st District seat. Republican incumbent Eric Skrmetta, who represents conservative areas in and around New Orleans, made much of opponent Forest Wright’s recent conversion to the GOP.

He even enlisted one of Congress’s top Republicans, 1st District U.S. Rep. and Majority Whip Steve Scalise, to the cause. “I’m fighting it in Congress, but we need Eric Skrmetta on the Public Service Commission to help me stop Obama’s EPA nonsense,” Scalise said in a television ad, over typically grainy video of the president. And in a take-off of the famous “Hope” poster from the first Obama campaign, Skrmetta sent out a mailer picturing the president and Wright side-by-side. The caption? “Nope.”

Wright came close Saturday night, but Skrmetta survived to serve another term.

There were national overtones in even the most localized of races, for School Board, at least in Jefferson Parish.

Four years after a business-backed slate won a majority and enacted an agenda in line with the national “reform” movement — a key component of which was weakening the teachers union’s hand on issues such as teacher assessments, layoffs, merit pay and collective bargaining — the union came storming back. In the days leading up to the November primary, the American Federation of Teachers’ political action committee put up nearly $450,000, a huge amount in these generally low-budget races, to promote the local affiliate’s slate.

The group got the result it wanted: The results of Saturday’s runoff cemented a new, union-friendly majority.

Perhaps there’s nothing surprising about the Jefferson Parish fight. Local and state education policies in Louisiana have become intertwined with the national debate over everything from the growth of charter schools to the Common Core educational standards. And Gov. Bobby Jindal’s stances on these and other topics are clearly tied in with his presidential ambitions — so much so that several of the candidates to replace him next year have pointedly promised not to let national issues dictate their agendas.

Maybe so, but as we get ready for the next round of campaigns, you can bet that they, and candidates for down-ballot offices, will be tempted to follow the lead of this year’s candidates. It’s hard to argue with success.

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