Congress’s eleventh-hour compromise on Tuesday settled tax questions for most Americans, but lawmakers postponed for two months the contentious issues of how and where to reduce federal spending. That leaves scores of Massachusetts institutions and businesses in limbo, unsure of whether they can count on government contracts and grants that support their operations.

“The riskiest part of the ­fiscal cliff still remains for Massachusetts,” said Martin ­Romitti, senior vice president at the Center for Regional Competitiveness in Washington.

Janet Ceddia, president and owner of Security Construction Services, a general contractor in Hudson, laid off several employees recently because of a slowdown in government work, including delays in a $3 million contract to rebuild an Army firearms range still in operation at the former Fort Devens. The Pentagon and other federal agencies have put projects on hold until Congress acts.

“I didn’t have the work, and I couldn’t suffer bleeding costs,” Ceddia said Wednesday. “Congress may have kept the financial markets from going into a total tailspin, but I’m in no better place than I was a week ago.”

Congressional leaders carved out a hard-fought tax plan that raised taxes on top earners and Social Security payroll taxes for most Americans.

The agreement sent stocks soaring; the Dow Jones industrial average added 308.41 points to close at 13,412.55, a gain of 2.4 percent, the largest point gain in more than a year. The S&P 500 and Nasdaq stock indexes notched even sharper gains of 2.5 percent and 3.1 percent, respectively.

Yet the compromise was far from comprehensive, and some of the most bitter budget battles lay ahead. Congress delayed more than $110 billion in automatic spending cuts set to take effect Jan. 1, extending their deadline for two months in the hope of finding a more measured approach to lowering the budget deficit.

But that delay also heightens the likelihood of another tortured political showdown in March, when the federal government also will face the limit on its borrowing, known as the debt ceiling. Congress must vote to raise the debt ceiling, which Republicans have used as a means of forcing spending cuts from reluctant Democrats.

Massachusetts has much at stake in the outcome. The state is the fifth-highest recipient of Department of Defense money, which exceeded $14 billion in 2011, according to an analysis by the University of Massachusetts. Another $7.7 billion in federal funding was allocated to the state’s colleges, universities, and hospitals for research and development, including large grants from the National Institutes for Health.

These cuts would come as the Massachusetts economy is slowing. The state unemployment rate has risen a half-percentage point since the summer, to 6.6 percent from 6.1 percent in July.

Romitti, who coauthored the UMass analysis, said the scale of cutbacks under consideration could drag the state into another recession. If Congress allows the automatic cuts to take effect, some 50,000 jobs could be lost in the first few years, including many high-paying jobs in the state’s research and technology sector.

University of Massachusetts officials said the state system could lose as much as $32 million in federal research funding if the current plan goes into ­effect unchanged. Dana-Farber Cancer Institute in Boston is reluctant to begin new projects with NIH funding up in the air.

“It worsens the uncertainty,” said Karen Bird, Dana-Farber’s chief financial officer. “We’ll be in an anxious state for a couple more months.”

Officials at the Massachusetts Institute of Technology, which receives about $1.3 billion in federal funding a year, warned researchers last fall to prepare for potential budget cuts of as much as 9 percent, or more than $100 million, if the country fell off the fiscal cliff. University officials and researchers are still waiting for Congress to act on spending ­issues before they making long-term commitments to projects and hiring.