Right now, there's no timer if you don't do anything bad. But any on-site crime starts a timer ticking down, based on steps and other actions. More crimes or attracting funny looks will increase the speed the timer decrements. Once it hits zero, you get the "conservatives suspicious" status at the top of the screen, and one failed disguise roll and the alarm goes off. If you keep making your disguise rolls every time, you can stay here forever without consequence, but you have zero room for error: one failed roll and the alarm goes off and violence breaks out.
After the alarm goes off there's another timer, this one counting up, counting the number of turns the alarm has been on. As it increases, the number of pursuers who will chase you when you leave the building increases, and eventually, if you wait around long enough, you'll hit the "Massive Conservative Response" and the building will be stormed by the police or some other unit. Which people respond depends on the location: the public park gets swamped by cops, AM Radio gets rushed by hordes of angry rednecks, Corporate HQ calls in private mercenaries, the Police Station brings out their big guns and deploys SWAT teams, etc.. Some locations attract particularly fast massive responses, most notably the Police Station, Prison, and Courthouse. You can stay as long as you want past the massive response, and there aren't any more events besides yet more enemies showing up, but the lethality of combat increases dramatically at this point and it's usually best to get out fast.