It is usually not a fixed dollar amount ... most often, it's a range of desired funding versus the time for the venture to become stable (that is, consistently break-even). Too little money and the venture will not survive, too much money and some will be wasted. The optimal amount is a trade-off with the length of time it will take for the venture to become stable (that is, consistently break-even week after week). The management team needs to know what results they can deliver if the investors do pony up the requested level of funding ... and what could happen with less money raised, or more money raised. The results are usually, but not always, a change in the time to become a stable company.
A "lean" startup is a special case ... the venture is basically trying to launch and operate below the minimum level of funding need to become stable. Think of it as an experiment. There are things to be learned in a lean venture, and often the most important lesson is that the venture just isn't going to make it without a critical mass of resources. Another lesson is that money isn't the only answer. Too much money can actually be a bad thing, but usually not as bad as too little!
In general, the more money raised for a new venture, the faster that venture can become stable up to a point. Investors will often ask the range of funding the venture is seeking. What's the minimum level of funding to get it going and sustainable, and how long will it take? What's the minimum time to become stable, and how much funding will it take? And finally, ... what does the venture team believe is the optimal trade-off between time and money?
A little humor: I once made a presentation to a group of "friendly" investors. Call them "friendly" because they already knew us (the management team, had put a good deal of money into our venture, and were (currently) satisfied with the results. Now, we were seeking to raise new money for a spin-off. In my presentation, I said we needed to raise $x million and it would take us about y months to get the new venture stable (consistently break-even). One of the investors asked what could happen if they put in half the money we were seeking. I said the venture could still probably make it but it would take so many months longer to stabilize, but that level of funding was still above the failure threshold. The same investor then asked what could happen if we were able to raise three times the money we were seeking. The "wise guy" in me came to the surface. I said that level of funding was way above the amount needed to make it to the shortest possible time to stability, and that the management team would take the excess funds and all buy Porsches because the venture didn't need the money! I point out again that these were "friendly" investors and I knew they had a sense of humor! They didn't throw me out the door. Rather, they had a good laugh and said those were exactly the "right" answers ... they were just testing the management team to make sure we knew where the endcaps were! --Jim