To go to 100x, that means about $23,000. 

First, those with bitcoins must have greater incentive to keep them in bitcoins rather than exchange them for fiat.  This means that the reasons to move back to fiat are greatly reduced/eliminated.  I'm thinking if major credit cards started accepting bitcoin-based payments that might do the trick (even if they converted to fiat when you paid them, this means bitcoin savings accounts could replace bank savings accounts for the general public without loss of functionality when you need to buy with "cash").

That might be enough, but assuming that happens there is still an influx of mined coins that have to be accounted for.  At the current 3600 BTC/day, $23,000/BTC, that's $82,800,000 worth of coins being mined each day, or $30.24 billion/year. 

For comparison, about 2500 tons of gold is mined each year, which equates to about 80 million ounces.  At $1,205/ounce, that's $96.4 billion.  So Bitcoin would have to be about 1/3 as popular as gold if it were to happen right now.

However, it gets easier to maintain the price each time the mining rate halves.  Here's the amount per year after the upcoming halvings needed to offset a $23,000/BTC price:

  current - $30.24 billion/year   1/3 as popular as gold
  2016    - $15.12 billion/year   1/6 as popular as gold
  2020    - $7.56 billion/year    1/12 as popular as gold
  2024    - $3.78 billion/year    1/24 as popular as gold
  2028    - $1.89 billion/year    1/48 as popular as gold
  2032    - $0.95 billion/year    1/96 as popular as gold