Before you start celebrating that gas is cheap this summer, consider the implications of slowing global demand for oil. 

FORTUNE – During the past few weeks, a plunge in oil prices has resulted in lower gas prices nationwide. In some parts of the U.S., prices at the pump have fallen below $3 a gallon.

Cheaper gas would normally be a welcome relief, but there are several downsides at play. Declines in oil and gas have signaled a weaker economy in the U.S. and across the globe. And while paying less to fill up the tank will mean extra savings for U.S. consumers, it's questionable how much those savings will boost overall confidence and translate into more spending.

Oil prices recovered some this week, but sharp declines in May still hover over the market. On Friday, oil plunged nearly 4% after a bleak report on U.S. jobs growth and slowing manufacturing activity in China raised worries about a slowing global economy and softer demand for oil. Gas prices hadn't fallen below $3.60 a gallon since mid-February, but over the weekend, the national average dropped to $3.585 a gallon. At a few stations in South Carolina and Virginia, prices fell just under $3 a gallon.

Nationwide, gas prices hovered at $3.61 a gallon on Tuesday, down 18.2 cents from last month and 16.2 cents lower than last year. Brent crude, used to price international oil, is struggling to stay above $80 on the New York Mercantile Exchange -- earlier this year it was going for more than $100 a barrel.

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Economists watch gas prices closely, as they consider anything above $4 a gallon the point at which costs start crimping consumer spending, which largely drives the U.S. economy. As a rule of thumb, about $1.2 billion in extra spending is typically generated for every one-cent per gallon decline for the year, says Chris Lafakis, economist at Moody's Analytics who specializes in energy and financial markets. But such savings may not be enough to offset the world's economic malaise that has also driven oil prices lower.

For one, Greece could leave the euro any week now as European leaders struggle to find a solution to its debt crisis. In China, the latest signs point to a slower growing economy. And evidence is building that the U.S. economy has entered a soft patch. All this has unnerved investors, who've increasingly questioned the strength of demand for oil and other energy-related products.

Analysts predict gas prices will likely stay subdued at least through the summer, but it's uncertain if that will be enough to make consumers feel any better about spending more.

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In April, U.S. retail sales rose only 0.1%. Even after excluding gas station sales, consumers increased their spending on retail goods by just 0.2% as gas prices fell.

If anything, consumers appear mixed about their economic prospects. At one end, consumer confidence rose in May to the highest level since October 2007, according to the Thomson Reuters/University of Michigan Surveys of Consumers. Of course, that survey places more weight on gasoline prices than the Conference Board's survey, which puts greater weight on employment and showed consumer confidence fell to a five-month low during the same month.

Indeed, some consumers might find relief at the pumps. But for the millions of unemployed Americans, gas at even $2 a gallon probably won't be enough to change their behavior.