Federal workers returning to their offices Friday could find furlough notices sitting on their desks, but it will be a while before most of them are actually forced to take unpaid leave.

Agency heads have warned that $1.2 trillion in federal cuts that took effect Friday will force them to cut the hours of hundreds of thousands of federal employees to help save $40 billion by year's end.

But it can take a month or more to actually furlough a federal employee. And that means it's possible that President Obama and congressional Republicans could strike a deal on the so-called sequester and avert the across-the-board budget reductions before most employees miss a single day.

Unlike many private-sector employers, the federal government can't just give someone a pink slip requiring them to leave immediately. Before anyone can be forced to take unpaid leave, agency heads must first meet with labor union leaders to "bargain" over how the furloughs would work, according to Office of Personnel Management guidelines.

Once both sides reach an agreement, targeted employees will be notified that they will be furloughed -- in 30 days. The monthlong notification means it will be April before anyone is actually furloughed.

Furloughed employees would have to take at least one unpaid day off each week through September. Any employee who wants to fight a furlough can also file an appeal, further delaying the forced leave, but unions aren't sure that's a necessary step.

"If we have an agency who is working with us collaboratively and being very transparent and doing everything they can working with us to eliminate or mitigate the impact, and they're taking up our ideas about saving money and how to do it so that it's not in furlough days, then I would want to focus their energy and their time, and ours, on continuing to do that," said Colleen Kelley, president of the National Treasury Employees Union.

The furloughs could impact hours at national parks, wait times at airports and the quality of meat, said Stephen Fuller, an economist at George Mason University.

"It's like a snow day the first day, but at some point, it became very disruptive," Fuller said. "And pretty soon, local government is feeling it in their tax base."

Staff Writer April Burbank contributed to this report.