For election-watchers who think presidential races are always about “the economy, stupid,” it didn’t matter much what President Obama said in his State of the Union address Tuesday night. One way or another, the tepid state of the economy is going to make the presidential election a nail-biter.

If the economic recovery continued to putter along at its current rate, Obama probably would win 50.17 percent of the vote in November, according to a statistical model by Yale University economics professor Ray C. Fair, who has been studying the relationship between presidential elections and the economy for three decades.

The only politically viable action big and immediate enough to move the needle would be an extension of a payroll tax cut, which Fair predicted would boost the economy enough to add 1.6 percentage points to Obama’s electoral margin.

“The thing Obama doesn’t have going for him . . . is that he doesn’t have any real strong growth quarters,” he said, adding that “2012 is really critical. It does truly matter what the per-capita growth rate is in the next three quarters.”

Yet Obama doesn’t have many levers to pull. Few of the proposals he laid out Tuesday night — tax reform, expanded job training, infrastructure investments, energy-saving incentives for manufacturers, a home-refinancing plan — would jolt the economy before November.

And in any case, Congress is unlikely to pass many of them.

“The ideas may be good, but the ability we have to achieve the objectives is limited,” said Robert Reischauer, president of the Urban Institute and a former Congressional Budget Office director.

Other factors that are largely out of the president’s control — such as a spike in oil prices, the conflict with Iran or a new chapter in the European sovereign debt crisis — could deal setbacks to the U.S. recovery. On Tuesday, the International Monetary Fund slashed its forecast for global economic growth, although it left its prediction for U.S. growth unchanged at an anemic 1.8 percent.

Still, against the odds, Obama is making the campaign about the economy, casting his proposals as a matter of “fairness” — a word he used at least seven times Tuesday.

“We can either settle for a country where a shrinking number of people do really well, while a growing number of Americans barely get by,” he said, “or we can restore an economy where everyone gets a fair shot, everyone does their fair share, and everyone plays by the same set of rules. What’s at stake are not Democratic values or Republican values, but American values. We have to reclaim them.”

Jeff Shesol, a partner at West Wing Writers, a speechwriting and strategy firm, said: “We keep hearing about how populist these themes are . . . as though talking about economic opportunity is some left-wing obsession. This is as American an idea as you could come up with. This is a broadly popular belief system. When he talks about fairness, about opportunity, he’s occupying the center ground.”

The release of GOP presidential candidate Mitt Romney’s tax returns, showing that he paid an effective rate of just 13.9 percent on more than $20 million in income in 2010, played right into Obama’s theme, highlighting the low tax rates that many of the wealthiest Americans pay. Obama proposed ending all tax deductions, including those for mortgages and health care, for people who earn more than $1 million a year.

“The argument ends up being more than a matter of what’s fair and really also about what works,” said Austan Goolsbee, former chairman of Obama’s Council of Economic Advisers and now an economics professor at the University of Chicago. “The highest-income people had their taxes cut by trillions over the last 10 years, and it didn’t trickle down into faster growth or more employment. So the president has been arguing that it didn’t work the first time, so we shouldn’t do that again.”

What Obama argued Tuesday is that Congress should adopt his “blueprint for an economy that’s built to last — an economy built on American manufacturing, American energy, skills for American workers and a renewal of American values.” He said he would establish a “trade enforcement unit” to investigate unfair trade practices abroad.

But many parts of his plan are controversial.

Obama, who has tangled with the oil and gas industry, reiterated that he supports opening up 75 percent of the nation’s potential offshore oil and gas reserves for exploration, but he also proposed ending “taxpayer giveaways to an industry that’s rarely been more profitable.” Despite criticism of Energy Department loan guarantees, he said he wants to “double down” on clean energy.

He proposed to tax the vast pools of overseas corporate profits to try to persuade companies to move manufacturing jobs to the United States. But that would arouse the ire of many of the nation’s biggest and most influential corporations, which have been looking for tax breaks before bringing that money home. A handful of the biggest technology companies, for example, have well more than $100 billion parked overseas.

The president wants to put half the savings from the end of war spending into infrastructure, although many lawmakers want to devote all those savings to deficit reduction.

Obama also said he would ask Congress to approve a program that would allow homeowners who are current on their payments to refinance mortgages at the prevailing low interest rates. He said some of the administration’s proposed bank fees would cover the cost of the program. It’s another step for an administration that many housing experts say has not adequately addressed the deep and stubborn housing slump.

“I think it’s a good move,” said John Taylor, president of the National Community Reinvestment Coalition. “I think he’s getting it, that we have to save the property owner if we’re going to save the economy.”

Some of Obama’s supporters are daring to think that the economy might grow enough to convince voters that the nation is at least heading in the right direction. And on Tuesday night, the president claimed credit for a revived auto industry and for more private jobs being created in 2011 than in any year since 2005.

“American manufacturers are hiring again, creating jobs for the first time since the late 1990s,” Obama said.

Said Goolsbee: “If things continue like the last three months, that would be significant progress. The economy is almost certainly not going to be a big plus, but if it moves from one of the toughest things for the president to deal with to something not great but clearly improving, the implication for the president would be nothing but positive.”