If the userbase for Bitcoin doesn't increase, then logically the price would go down, as the total number of Bitcoins increases.

Thus, for $1,000/BTC to become reality, the userbase needs to grow at least ten-fold in a week. Or more realistically, about twelve-fold in a year. This would need an exponential increase, which is unlikely and could create a bubble like happened a few months ago.

The most likely path is a steady increase, higher than the effect of newly generated Bitcoins. This would mean $1,000 will take about 24 years.

However, fiat notes are printed all the time. This is not the worst part. Your savings can be lend out by banks eleven-fold. The same cannot be done with Bitcoins. Looking at all this from outside the box, you'd think that fiat currencies are more likely to crash to worthless than Bitcoins. In fact, several have! And Bitcoin never became worthless! So when reasoning that money is worth "people's trust x ( people using 2 )" and trust in fiat should stay the same (but fiat suffers inflation) and trust in Bitcoins should rise, then things speed up. $1,000 would 'only' take 4 years (just after the block decrease to 12.5).

This also means that the rise in value won't be a steady incline. Rather, every few months it will 'correct' itself as the increased trust in Bitcoins doesn't show up in the day-to-day exchange rate.