Here's the thing.... can you do the work in 2 weeks?
If you can't then what possible benefit is there to trying to retain a client with such unrealistic expectations? Or in other words, if someone asks you to do the impossible and they'll pay you.... no matter how much you may want to do it... it is impossible so you can't.
Be aware that many clients, even some savvy clients, aren't fully aware of what is involved in projects they may want completed. In my experience they will estimate based upon their timeframes in the past. However, many are aware that their estimate is just that - their estimate - and not real-world expectations from someone aware of all the details which will need completed.
It is also common for clients to negotiate timeframes from an unrealistic starting point. "2 weeks" is a common ballpark figure used. The client may be fully expecting you to return and state you need much more time.
In the end, the time you need is the time you need. I don't know about you but I can't make my brain work faster than it does. I can't make my body go without sleep and food for days on end. I can't make applications save faster than they do. I can't make servers load well constructed web pages faster than their processor allows. I can't make time move slower. I can't make gravity less invasive... I can't do the impossible. So I can't worry about retaining a client during estimations by trying to meet impossible goals.
When it comes to time frames..... Estimate what you need... not what the client expects. Then if you feel you may be able to shave a week or so off while working, do that. But it is generally good practice to ask for more time than you think you'll need, not less.
If you lose a project because of your realistic timeframes, and the client isn't open to seeing realistic figures, then it's not a good client to begin with. Remember your the expert when it comes to your work, not the client. Just because they want the impossible, it doesn't mean you should feel obligated to provide the impossible.