Yes, you can usually still drive your Jeep with a bad TPMS sensor, but you'll lose the early warning system that alerts you to low tire pressure. You're taking on more risk by driving on an underinflated tire without realizing it, so you should check your tire pressure manually and get the sensor checked soon.
Here's what's actually happening when that warning light comes on and stays on. Your Jeep's tire pressure monitoring system is designed to flag dangerous pressure drops before they become a bigger problem, such as a blowout or uneven tire wear. When a sensor fails, whether it's a dead battery or physical damage from a pothole or curb strike, you lose that safety net for that particular tire. Your Jeep will still drive normally in the short term, and you won't damage anything by continuing your daily commute around Ann Arbor. That said, you're now flying a little blind. If that tire slowly loses air over the following weeks, you might not notice until you feel a change in handling or see visible wear.
You should be especially mindful of this heading into a Michigan winter. Cold temperatures cause tire pressure to drop naturally, sometimes by several pounds per square inch over the course of a cold snap, and normally your TPMS would catch that shift for you. Without a working sensor, you're relying on your own habit of checking pressure with a gauge, which most drivers admit they don't do often enough. If you notice your Jeep pulling to one side, feel an unusual vibration, or see a tire that looks lower than the others, don't wait, pull over and check it or bring it in.
It's also worth mentioning that if your Jeep has multiple sensors failing, or the warning light is flashing rather than staying solid, it can indicate a bigger issue with the whole TPMS module rather than just one sensor, and that's worth having diagnosed properly rather than guessing.
While driving with one bad sensor won't strand you on the side of Washtenaw Avenue, it's not something to put off indefinitely, especially with unpredictable Michigan road conditions. If your Jeep's tire pressure light has been on for a while, the team at Hoover Street Auto Repair in Ann Arbor can quickly diagnose whether it's a simple sensor replacement or something else going on with your TPMS. Their technicians work on Jeeps regularly and can get you back on the road with confidence that your tires are being properly monitored again.