Major changes are coming to Chicago's airports on Friday, as airlines are set to begin cutting the number of flights in the air as part of a mandate from the U.S. Department of Transportation to reduce air traffic by 10% at 40 "high-volume" airports.

United Airlines outlined its plans Thursday afternoon, announcing a 4% reduction in flights at O'Hare International Airport starting Friday, or about 23 round-trip flights. American Airlines also said it will reduce its scheduled flights by 4% from Friday through Monday.

United will stay at 4% reductions for four days, and then gradually increase cuts until they hit a 10% reduction next Friday – a date they said was mandated by the Federal Aviation Administration.

The airline said these are the kinds of cancellation numbers they'd see in a light snowstorm.

Most flights arrived as scheduled at O'Hare on Thursday, but airline leaders and passengers have begun bracing for turbulence.

The FAA announced this weekend will mark the start of reduced air traffic capacity across 40 of the country's busiest airports – including O'Hare and Midway airports in Chicago.

Major carriers, including United, American, and Delta, have begun offering passengers free flight changes and cancellations.

The CEO of Frontier Airlines posted on LinkedIn that he would "suggest passengers buy a backup ticket on another carrier that departs after the first ticket."

CBS News travel editor Peter Greenberg said airports might not be much of a mess when the flight reductions begin on Friday, but could get messier by Monday, when most of the cancellations will kick in.

"I want to caution everybody, as more controllers don't show up for work, that 10% cut may be a 20% cut. And you're not just dealing with ground holds. At that moment, you may be dealing with ground stops, which nobody wants," Greenberg said.

Greenberg said anyone thinking of booking a flight should know that, if the airline cancels it, they'll get a full refund, but if the traveler cancels it themselves, they might only get a credit, not a refund.

DePaul University professor and transportation expert Joe Schwieterman said the move by the FAA is unprecedented and uncharted waters for airlines, particularly coming out of a slow travel season in October.

"It's on such short notice, so airlines' options are limited," he said. "Southwest Airlines has a particular problem, because they fly all [Boeing] 737s, and nearly all those planes just cycle around the country. So you can't simply take a flight out of the schedule without that plane being in the wrong place, and crews getting stuck, and so forth."

A sure sign of eager anticipation, a mother from the Milwaukee area checked the flight boards at O'Hare on Thursday for updates on her son's arrival. He arrived on time, but they're already thinking ahead to his departure.

"I am concerned about the return, because with the announcement about cutting 10% of the flights, flying back is a concern. He's got to get back for work on time and so forth. It's a concern. So, yeah," she said.

Matt Lindner said his Southwest flight from Dallas to Midway was canceled, forcing him to fly home hours later than planned.

"I am cautiously optimistic. I am not thrilled about the fact that I'm not going to be able to put my daughter down to bed the way that I was supposed to," he said. "Our government has to do a better job of taking care of the people, because that's how it's supposed to work, and not the other way around."

United said, when choosing which flights to cancel, they selected routes that are mostly small planes headed to regional destinations. They looked at passenger counts, and which routes would be easiest to rebook. No international flights or routes between hubs are affected. 

"They'll find out tonight if the cancellations have already gone in, and some have already," United spokesman Omar Idris said.

Greenberg said the economic consequences of the flight cutbacks "cannot be overstated."

"You're dealing with planes that are out of sequence, flight crews that are out of schedule, planes that are not in position, and if people can't connect flights, therefore you're dealing with cancelled meetings, lost revenue, not to mention lost ticket revenue for the airlines, which will have a bad quarter because of this," he said. "So as these economic consequences increase in severity, then you're going to see bipartisan support; meaning, if a plane is cancelled, you're angering both Republicans and Democrats. It's not political anymore, and my guess is in the next four to five days, if this continues, the shutdown will end."