The unemployment rate dipped to its lowest level in nearly three years last month, good news that on Friday rippled through rival presidential campaigns whose prospects could hinge on the pace of the economic recovery.

Unemployment has declined in four consecutive months, to 8.5 percent, its lowest level since the president’s second month in office. However fragile, it is the kind of trend that President Obama is counting on to convince voters that he deserves a second term in the White House.

But Obama’s advisers reacted to the report with hard-earned caution. They have not forgotten 2010’s “Recovery Summer,” which began with a spate of presidential groundbreakings meant to highlight the healing effects of the economic stimulus bill only to have the jobless rate go up, not down.

They also are concerned about economic forecasts indicating that things could get worse before they get better. A surge in oil prices, a recession in Europe or a slowdown in China could derail the jobs recovery and, with it, Obama’s reelection hopes.

“From the president’s perspective, an acceleration of positive trends is the best he is going to get. He is not going to be able to get the nation back to full employment this year,” said Jared Bernstein, a former member of Obama’s economic team. “But, given all the false starts, you certainly can’t get unduly optimistic.”

Remarks from the White House and from Republicans were indications of how the two sides will portray the economy to the public. Obama and his aides highlighted the trend of declining unemployment. Republicans latched onto the still-high numbers of Americans out of work.

GOP strategists acknowledged that an improved labor market could complicate their most potent argument against Obama. But they pointed out that at several points in the past couple of years, the economy has seemed poised for substantial growth and then stalled.

“We have to ask ourselves, now for the third time, do we have a sustainable recovery that is organic?” said Tony Fratto, a former aide to President George W. Bush and a partner at Hamilton Place Strategies, a D.C. consulting firm. “The public is skeptical of short-term economic data. It is going to take a longer period of recovery before people believe it is sustainable.”

Obama focused on the improving employment picture during a speech Friday at the Consumer Financial Protection Bureau.

“Altogether, more private-sector jobs were created in 2011 than any year since 2005,” he said. But he also acknowledged: “We have a lot more work to do.”

There are 1.7 million fewer jobs in the country now than when Obama took office, according to government data, a fact often cited in the Republican criticism of the president’s economic stewardship.

Yet employers created 200,000 jobs in December, a pace that, if maintained through the November elections, would enable Obama to say he is a net job creator as president.

“What really counts politically is the direction things are moving,” said Mark Mellman, a Democratic strategist. “People care more about the direction of change than the absolute level. Optimism is up, and that is good for the incumbent.”

The jobs data follow reports showing rising consumer confidence, an improving manufacturing sector and healthy auto sales.

Obama attributed the improving economy, at least in part, to the payroll tax cut, which saved families an average of $1,000 last year. Congress has agreed to extend the cut through February after a bruising partisan battle, but Obama called on lawmakers to approve it through the end of the year to avoid the risk of stifling the recovery.

“There should not be delay. There should not be a lot of drama. We should get it done,” he said. “We have made real progress. Now is not the time to stop.”

Republican presidential front-runner Mitt Romney called the improvement in the labor market too little, too late.

“Of course it is good news fewer Americans are out of work, but thirty-five consecutive months of unemployment above 8 percent is no cause for celebration,” Romney said in a statement. “America deserves better. Eventually our economy will recover, America always does. But President Obama’s policies have slowed the recovery and created misery for 24 million Americans who are unemployed, or stuck in part-time jobs when what they really want is full-time work.”

Even some of Obama’s political supporters pointed to factors that could make the improvement fleeting.

A major reason that the jobless rate has gone from 9.9 percent to 8.5 percent in the past two years is that many thousands of people have given up looking for work. If the workers who dropped out were counted as unemployed, the jobless rate would be a full point higher, said Heidi Shierholz, an economist at the liberal-leaning Economic Policy Institute.

Meanwhile, 5.6 million Americans — 42.5 percent of the unemployed — have been jobless for more than six months. Also, minority joblessness has remained at catastrophic levels: The black unemployment rate was 15.8 percent in December, and the jobless rate for Hispanics was 11 percent.

Those sobering statistics have helped subdue the White House reaction to the improving jobs picture.

“I have not seen any celebrations going on. We recognize that this is a very deep hole that the economy is digging out of,” said Alan B. Krueger, the top White House economist. “The problem has built up over decades, and the job losses from the recession that started at the end of 2007 were very large,” Krueger said. Friday’s “report and other information coming out only suggest that the economy is headed in the right direction.”

Staff writer Ylan Mui contributed to this report.