I knew it would be impossible without doing overtime, and I wasn't willing to put myself in that position. I was so taken aback that I said: "Uh I'll try, but I finish in half an hour."
You did everything right, but you could have been more assertive. If you know that the task takes one hour, and you only have half an hour or less, you shouldn't say: “Uh I'll try,” but rather “Of course, I'll start it right after the meeting; however, the task would probably take one hour, so I'll have to continue tomorrow.”
If the manager insists on doing it today, you kindly reply: “I'm very sorry, but I can't leave late today, so I would only have half an hour if the meeting doesn't run late.” If he continues to insist, you should respond more firmly: “As I said, the task will take an hour, and I only have half an hour. Do you want to give it to somebody else? If not, what else do you suggest?” Any suggestions about you staying late should be dismissed very firmly: “As I already said one minute ago, I can't stay late today.”—the person is interfering with your private life, and any suggestions to stay late when you explicitly told that you can't do that are impolite.
Remember that your manager can decide what you will do, but he can't decide how fast you'll do it. He can't just assert that a three hours task can be done in one hour; putting more pressure on you won't make you think faster:
Lister's law: People under time pressure don't think faster.
If he insists on spending less time, invite him to reconsider the task itself. For instance, if you need to design a feature, you may suggest changing the feature so that it would be easier to implement, or cut a part of it, keeping only the essentials. Here too, a manager who refuses to discuss the subject and insists that you have to perform the original task in shorter time without should receive a clear and immediate feedback that this is not how things work. Doing otherwise, like telling: “I'll see what I can do.” would inevitably get you in trouble. Even formulations such as “Oh, I'm really sure I won't be able to do it in just an hour, but I may try.” would be misinterpreted, and the manager will be angry at you that you haven't kept your promise of finishing the task at time.
Needless to say the meeting ran overtime and I didn't do it. I've now done it today, but I'm concerned about future incidents arising.
You haven't mentioned the most important part. You missed the deadline, and then what? What was the reaction of the manager?
Reading your description, I had an impression that the manager may simply be trying to motivate you. I didn't say he was doing it right, but this is what some managers do. “I want this and that yesterday, and no compromises with the quality!” Such manager puts a lot of pressure, but he knows that the team won't be able to follow anyway, so when things are late, he doesn't blame anyone—he expected the thing to be late anyway.
If this is the case, there are specific techniques to deal with such persons. In most cases, it comes at simply discussing the issue with the manager, explaining the negative consequences his choice has on the morale of the team. However, you have to study the person well enough—some won't like a direct feedback like that.
If, on the other hand, the manager blamed you for finishing the task later than expected, this is probably a direct consequence of your “Uh, I'll try.” As stated above, you have to be firm when it comes to the delays and avoid misinterpretations.
