I addressed much of this in the white paper, but will address it here to.
As demand increases, the witnesses will lower the interest rate until it reaches 0. The lowering of the interest rate should be done only periodically (at most once per month). This gives markets a chance to adapt to the new rates.
If demand surges beyond that, witnesses can adjust the price feed to give less steem per steem dollar. A side effect of this will be to increase the rate of issuing Steem Dollars.
Effectively, a surge in the demand for Steem Dollars will show up as a surge in the price of Steem.
Thanks, I totally forgot the interest rate. I wrote the post quite quickly, didn't even checked what whitepaper said.
But I don't think it will make much difference in this situation. If there is huge demand, people don't care how much they get interest. Probably most of them are just fine with 0 %. They are mostly looking for a way to protect their wealth in a bad economic situation.
Sudden huge demand is possible because SD is so useful: it's free to use, it's fast, there is no limits who can use it and how it can be used. This might cause a situation where demand for SD is bigger than demand for USD (if transfers for real fiat currencies are limited).
What's going to happen if price is pegged to SD=USD, but actual demand is bigger for SD?
Similar situation has happened earlier with coins that have been made with precious metals, but later changed to cheaper material while keeping the same nominal value. This has made earlier coins much more valuable, but that's not possible with SD (if the peg mechanism holds).
My guess is that because arbitrage will be possible through different ways, the peg will hold and it will cause price of steem to go up. After all, steem is the currency that is supposed to take all volatility while SD is stable.
So... If the value of Steem will go up because of huge demand for SD, it means that the blockchain will create more SD. But this will not be given to those who demand it. Newly created SD will go for writers.
This might cause a situation where blockchain is paying huge sums for writers, which will of course incentivize more people to write, which will make Steem more popular and it will cause the price of Steem to go even higher.