In particular, Newt Gingrich has promised voters he’ll bring prices down to as low as $2.50 a gallon. The increasingly overlooked candidate vying for the GOP nomination has been harping on the “Drill baby Drill” mantra, arguing that raising energy production at home will lead to lower gas prices. Meanwhile, Rick Santorum has warned voters that prices could approach more than $5 a gallon. And even though Mitt Romney’s campaign has reportedly insisted he doesn’t focus on the issue, he nevertheless lashed against the administration’s approach to oil and gas development while campaigning in oil-rich North Dakota.

Consumers are influenced by gas prices, but history has shown that what voters pay at the pump won’t necessarily help unseat an incumbent’s party.

For one, the majority of voters don’t narrowly target the president for higher gas prices. They actually spread the blame, at least according to a recent Pew Research Center-Washington Post poll. It found 18% blaming the Obama administration, while 14% held oil companies responsible; 11% felt unrest in the Middle East was to blame and 38% gave a variety of other explanations – from Wall Street traders and speculators to greed.

Besides, gas prices aren’t the biggest concerns for voters, according to a recent Wall Street Journal/NBC News poll of likely voters. Only 8% of respondents listed higher energy costs including gasoline as the top concern. Jobs, economic growth, the deficit and health care topped the list.

MORE: Payroll tax cut, meet $4 gas

Of course, higher gas prices influence many other parts of the economy. During the run-up of the last presidential election, gas averaged upwards of $4 a gallon –typically the point at which it starts significantly crimping on consumer spending, which makes up about 70% of the U.S. economy. Research has shown that the spike might have even helped send the economy into the Great Recession, which started December 2007 and ended in June 2009.

In the 2008 election, Obama even played the gas card, blaming oil companies for the spike. He won, but it would be overly simplistic to blame gas prices for the incumbent party’s loss. The nation was going through several economic shocks, from the housing market crash to a banking crisis that taxpayers ended up grudgingly paying hundreds of billions of dollars to fix. Many factors beyond gas prices swayed the election.

Admittedly, in 1980, then President Jimmy Carter lost his re-election bid to Republican Ronald Reagan as the nation was coming off the energy crisis and gas prices were high.  It would be easy to blame fuel costs, but it’s hard not to wonder if there were bigger underlying factors at work. The Carter administration dealt with a period of international stagflation – that is, steadily rising prices in the face of weak economic growth. Another major factor was the Iran hostage crisis, where American servicemen died after U.S. officials attempted a rescue operation.

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So if the direction of gas prices isn’t the big influencer, what is?

Unemployment might have something to do with it — no U.S. president since Franklin D. Roosevelt has won a second term in office when the unemployment rate on Election Day was higher 7.2%. But unemployment seems like an arbitrary metric.  Reagan was re-elected in 1984 with the jobless rate at 7.2% on Election Day, but it could be that voters gave him credit for lowering bringing unemployment down from its peak of 10.8%. Today’s unemployment rate, at 8.3%, is down from well above the 10% peak recorded in October 2009.

Economists have countless models that show what influences voters. Economist Douglas Hibbs suggests under his “bread and peace” model that it all boils down to two things: How rich voters feel, and the number of military casualties.

This doesn’t necessarily mean good news for Obama. Under the model, Hibbs notes if the presidential election were today, the incumbent would garner less than half, or 45.5%, of the national vote. This comes as disposable personal income has grown 0% during the first 11 full quarters of President Obama’s term. Over the same period, U.S. fatalities in Afghanistan totaled 1,234 or 4 per million of population, he notes.

And Yale University economist Ray Fair’s model adds to the argument that gas prices have little to do with presidential election outcomes. The model finds that three factors, in particular, weigh heavier: The growth of real per capita GDP during the first three quarters of the election year, inflation during the last term, and decent real GDP growth per person (more than 3.2%) during last term.

“As of this writing the economy in 2012 looks like it will be okay, but not great, which means a close election – essentially too close to call,” Fair wrote recently.

So if Republicans really want to poke Obama, they might do better reminding voters to look at their pay stubs. And if Obama himself wants to help his campaign, perhaps he might want to remind voters how much the unemployment rate has declined since the peak of the crisis.