Many managers like to negotiate. They treat everything as a negotiation opportunity. In fact, many managers believe that negotiation is their most important skill, and that they can negotiate their way to any goal. If you want to keep them friendly, then you have to play the game; otherwise they get annoyed. Like traveling to other countries, you might need to haggle with the natives. It's just their way.
Accept the probability that what you might initially be asked to do is actually just the first round in a negotiation, and not some wildly deluded expectation. A manager's initial request is a like a car's sticker price: both parties know the real price is something different.
Also bear in mind that a manager's job is to minimize costs and time-to-completion, and to maximize the output of developers. Don't get offended when a manager tries to do that. Managers will push hard, but they don't want anyone to provide estimates that can't be met. Just hold to your estimates and politely make it clear that your estimates are not going to change unless the scope of work changes.
Some bad managers do want estimates that cannot be met (or at least which have little chance of being met), the estimate gives such managers a bit of political cover when things go wrong. "I know the project is late, boss, but JoeEngineer? here told me that his task would take two weeks, and it's taken him a month. It's his fault." Despite the fact that the two-week estimate was extracted from JoeEngineer? under duress of some sort.
Fortunately, that seems to be rare.
If a manager insists upon negotiating over something you think is non-negotiable (estimates, for example), quickly find something else to negotiate (team members, office space, donuts, whatever). This gives the managers the chance to do their thing, and gives them a sense that you are making an honest effort to be reasonable and to meet them halfway.
Developers in this situation are often intimidated and feel pressured to give answers that the asker wants, but there is really no need to feel that way. Just refuse. Once the managers see that you won't budge, they'll give up. Remember that it is very, very rare for someone to be fired or otherwise punished for giving an unpopular estimate. Given the choice between being fired or making promises you can't fulfill, being fired is better (there's a good chance you'd be fired for failing to fulfill those promises anyway).
If you do give a number, that is going to become The Number. Managers like hard numbers, and all qualifications ("probably", "more than", "less than", "ball-park", "rough order of magnitude") will be ignored or forgotten. So don't give out any numbers that you aren't willing to live with or to apologize for.
See also NegotiateEstimates, HelpYourManager