The debt-ceiling agreement struck over the weekend does not directly require cutbacks in the federal workforce or employee benefits — news that added to the relief of government workers Monday. But more angst and anxiety might be up ahead.

Should the agreement be signed into law, its plan for a two-stage cut in the federal budget could have implications for employees at each step.

“I am pleased to see that the deal does not include any immediate cuts to federal pay or pensions,” National Treasury Employees Union President Colleen M. Kelley said in a statement Monday. “However, the impact on the federal workforce remains uncertain and agencies are likely to face reductions in their budgets.”

Kelley was one of several union leaders who voiced concern about the potential fallout from the deal.

The first step in the agreement would be to set a series of caps on agency spending over 10 years, beginning with the fiscal year that starts Oct. 1. The caps would affect spending in defense as well as non-defense agencies.

Although government spending still is projected to rise, the increase would be smaller than had been projected, by about $900 billion over that period. The measure does not specify amounts for individual agencies or programs, leaving that issue to the government’s budget process. Agencies would have to decide how to live within the amounts available.

Depending on the severity of the budget restrictions, agencies might have to resort to steps such as furloughs, hiring freezes and layoffs. But that is uncertain at this point.

Under the plan, certain programs would have some protection, including disaster relief and efforts to detect fraud in disability and health insurance programs. Further, the caps would not apply to spending for the wars in Afghanistan and Iraq.

The second step of the plan would be the creation of a special House-Senate committee tasked with finding up to $1.5 trillion in savings. The regular congressional committees that oversee such programs could make recommendations, by Oct. 14, but would not be required to do so.

The measure does not specify potential targets, but the special committee could examine the numerous ideas for reducing federal benefits that have been in circulation for months. Those have included extending the general pay freeze beyond 2012, increasing the employee contribution to retirement plans, cutting federal employment through partial hiring freezes, reducing retirement benefits for new retirees by changing the way those benefits are calculated, and making cost-of-living adjustments less generous for all retirees.