Chaffetz, dressed down in jeans and a collared shirt, proudly points out that he's one slot higher than Lee in the upgrade line.
"I'm reconsidering this seniority argument," jokes Chaffetz, who contends, in more serious settings, that seniority in Washington isn't all it's cracked up to be.
On Thursdays, this Delta flight is the shuttle for a slew of members of Congress. It's the lone direct flight between Reagan National Airport and Salt Lake City, and, for many lawmakers, the quickest option to get to the Intermountain West from the nation's capital.
Lee and Sen. Orrin Hatch usually are on board, sometimes with senators from Idaho, Wyoming and Montana. The roster also includes Chaffetz and Reps. Jim Matheson of Utah, Doc Hastings of Washington and Raul Labrador and Mike Simpson of Idaho.
They might as well call this flight Congressional One.
In the terminal before boarding, the lawmakers are interspersed with the tourists sporting their new D.C. garb and business folks eager to be on their way. The ties and congressional pins are gone, but the members are still recognized.
"I'll vote for you again," says a woman as she passes Matheson, likely unaware that the six-term congressman is running in a new district this time around and that she may not be able to keep her promise.
"You see a lot of the same people," Matheson says of the weekly trip. "There are a lot of frequent fliers on this flight."
Utah's lawmakers are among those who have racked up tens of thousands of miles. Back-and-forth weekly flights will do that and that's where this nonstop offering comes in handy for the delegation.
Reagan National Airport is a short drive from the Capitol, much closer than heading to Baltimore-Washington International about 45 minutes from the Hill or, God forbid, trekking out to Dulles International, an hour and seemingly a lifetime of traffic away.
"There's a big difference between Reagan and Dulles," Matheson says while holding court with his chief of staff, Meg Joseph.
A second nonstop flight between Washington and Salt Lake City has the members excited. Starting June 7, they will be able to dash to Reagan for an early-morning flight that will get them to Utah before 10:30 a.m. perfect for those times when House votes run late the night before and a great way to dodge layovers in Detroit or Minneapolis or Denver.
On this Thursday afternoon the typical time for members to jet out of town after votes Matheson boards first, followed by Chaffetz and a cadre of former and current congressional aides. Chaffetz lands a window spot in row 26. Matheson is three rows back, on the aisle. Lee, who had put his name in for an upgrade seat, doesn't make the flight, nor does Rep. Rob Bishop.
Sandy Mayor Tom Dolan and lobbyist Dan Hartman, fresh off a Washington visit, are farther back.
"I don't think the City Council will let me do first class," Dolan says, firmly planted in economy.
As for the members of Congress, taxpayers cover the flights when they're on official business which includes travel to and from Washington. And members get other perks, too, including free parking at Reagan National and being allowed to keep without paying taxes any frequent flier miles they accumulate.
Once airborne and cruising along at 37,000 feet and nearly 500 mph, the new "Mission Impossible" movie starts on the aging televisions sprouting from the ceiling. Utah's folks aren't watching, preferring to take the time to read up on a packet of documents or rest for a while.
Chaffetz, whose usual preflight checklist includes a Big Mac (no pickles, no onions), often logs into the $34.95-a-month wireless Internet and continues to work, turning the three-hour, 33-minute flight into office time.
A free Diet Coke and packet of pretzels or nuts later, the flight lands and taxis to the gate. The door opens, smart phones are switched back on and the congressional members gather their things most packing light because they have clothes at home and head for waiting cars.
On Monday, they'll be back to do the trip in reverse.