President Obama’s signature on a new two-year budget deal brings welcomed stability and a bit of fiscal relief for the federal government, but tough leadership challenges lie ahead as agencies and their employees deal with continued austerity and deteriorating worker morale in 2014.

The new budget promises $60 billion in relief from across-the-board reductions imposed by the so-called sequester, but the government still has to operate with less annual funding than it had before those automatic cuts.

As lawmakers try to divvy up the money with an omnibus appropriations bill due Jan. 15, labor groups are predicting pain for the federal workforce. They expect agencies to halt new hires, shrink through attrition, hold back on purchases of new equipment and reduce training, all measures they resorted to last year.

National Treasury Employees Union President Colleen M. Kelley said many agencies are “still in dire straits when it comes to adequate funding,” despite the new budget agreement. She noted that the Internal Revenue Service has seen its budget reduced by about $1 billion since 2010. The agency is dealing with increased responsibility under the president’s health-care law, which requires it to track who has complied with the individual mandate and who deserves tax credits to help pay for coverage.

Federal workers were major casualties of the ugly fiscal battles of 2013 as they faced a pay freeze in its third year, sequester cuts, proposed benefit reductions and a government shutdown that kept many employees from their jobs and paychecks for 16 days.

Meanwhile, government-wide satisfaction for the federal workforce fell for a third consecutive year in 2013, dropping to its lowest level since the nonprofit, good-government group the Partnership for Public Service began issuing its “Best Places to Work in the Federal Government” report a decade ago. It uses the federal government’s Office of Personnel Management employee viewpoints survey. The score for morale in “Best Places” slipped to 57.8 percent last year, compared with 60.8 percent in 2012 and a high of 65 percent in 2010.

OPM said in a November statement that its survey results, released that month, served as a warning about the consequences of budget cuts and fiscal uncertainty. “Without a more predictable and responsible budget situation, we risk losing our most talented employees as well as hurting our ability to recruit top talent for the future,” the agency said.

Max Stier, president and chief executive of the Partnership for Public Service, said fiscal uncertainty caused disjointed planning and confusion over worker expectations, ultimately contributing to discontentment within the workforce. “Congressional budgeting is the source of much of the management dysfunction in government,” he said.

One area in which federal workers will see relief this year is with pay, as their salaries rise by 1 percent as a result of an executive order Obama issued last month. The workforce went three years without annual raises after the president halted the increases in 2011 and 2012, followed by Congress extending the rate freeze through 2013. Workers were still eligible for performance awards and higher pay through promotions during that stretch.

NTEU and the American Federation of Government Employees have both said their priorities for 2014 include lowering the limit on compensation for federal contractors. The recent budget deal dropped the cap from $952,000 to $487,000 per employee, but AFGE said the amount should fall to about $230,700.

Stier said the government could help itself through the continued belt-tightening by operating smarter — for instance, by purchasing bulk products as a single, giant entity in order to save money. He also recommended that agency leaders seek advice from workers on how to get by on smaller-than-usual budgets.

“They need to engage the workforce in figuring this out,” he said. “The solutions are often going to be in the employees’ heads.”