Most people have already paid their taxes and just have to file some paperwork confirming it. Many people have overpaid and if they don't fill out that paperwork, the government gets extra money. The IRS isn't going to care much then.
If you owe a small amount of money (probably the most likely case) they are going to care, but it's just not worth their while to deal too much with it. By small amount of money, I mean like $100. At that point, they'll want you to pay it, but it might cost them more to get you to pay it than the $100. Having a staffer spend 3 hours dealing with you would probably wipe out that $100. So, they'll take measures to make you pay, but they aren't going to waste too much effort.
If you're underpaying your taxes by a good deal, they'll make your life hell if you decide to brush them off.
The IRS operates similarly to how you'd expect - some things are worth their time, others aren't. Yeah, there are always humorous stories about someone getting a bill for less than a dollar, but overall the IRS wants to spend its time chasing the money. That means going after the egregious violators who are rich because those are easy to spot and have the most benefit to them. Going after someone earning $50k who forgot to report $30 worth of interest income on one of their bank accounts just isn't worth it.