Gail Helt, a former CIA analyst suggests that due to the huge size of the balloon (and almost zero pressure difference between inside and outside) that shooting the balloon full of bullet holes would not bring it down quickly. It would just continue to drift very slowly to lower and lower altitudes (right into commercial aviation traffic) before landing.
From DW News' February 4, 2023 China's spy balloons: What's the geopolitical fallout?
These balloons are so huge that even that kind of - that number of ammunitions - that amount of ammunition set towards it is only going to cause a very very slow leak, and it's not going to come down immediately.
You can't just pop the balloon and it's going to go away.
Presumably the balloon's payload is both of great interest and deserving of some caution. It could have defenses, a self-destruct mechanism, or other undesirable materials so one might not want to simply destroy the payload with a missile, and yet one might not want it landing on the population either.
Thus once it's over the Atlantic an air recovery operation might occur, or now that the balloon is having its "15 minutes of fame" US authorities might even just let it continue and irritate/traumatize other countries for political benefit.
update 1: Then again, maybe not: Video appears to show suspected Chinese spy balloon being shot down reportedly an F-22 fired a single AIM-9 Sidewinder missile and apparently the blast fragmentation pattern from a proximity detonation was enough to rip the balloon wide open and allow the payload to fall into the ocean, and a recovery mission is on its way.
Hat tip to @tedder42's comment:
The Drive suspects the AIM9 was used because it has a laser fuze, not radar
Nice real-time video at Fox 13 Seattle's The moment the Chinese spy balloon was shot down, ordered by President Biden where the balloon is shredded.
Source: New York Times February 5, 2023 China Condemns U.S. Decision to Shoot Down Spy Balloon footage credited to Associated Press
update 2: From BBC's February 8, 2023 When a Canadian weather balloon went rogue:
"We asked the Canadian military if they would consider shooting it down, sending somebody out for target practice," Mr Sommerfeldt said.
A fighter jet had a ceiling of about 60,000 feet, he recalled and "the balloon, of course, was a lot higher than that".
Hoping to save the research, he asked them to shoot upwards and aim for the suspension point, where the release mechanism was for the package of scientific instruments, which were attached to a parachute.
According to news reports from the time, the Canadian CF-18s fired more than 1,000 rounds of ammunition at the balloon - the pilots refrained from using air-to-air missiles.
The volleys of ammo did not work.
"It wasn't enough to shake loose the release mechanism. They probably hit the balloon too. But those small bullet holes and a balloon that size would have almost no effect," Mr Sommerfeldt said.
It then drifted back towards Norway before finally landing on Finland's Mariehamn Island after what the Tribune News Service dubbed a "nine-day odyssey".
The instrumentation was sent back to Canada and reused (though there were some bullet holes on the instrument package and its parachute). Mr Sommerfeldt said.