If I have a net negative number of dice, how many clue tokens do I need to spend to attempt a roll?
You always gain bonus dice from clue tokens spent, regardless of how negative your actual ability check is.

So in your example you do not have to spend one to overcome the negative, then another to gain a dice, you would be able to spend one (or more) clue(s) to gain one (or more) dice.

From the rulebook (page 13 under Spending Clue Tokens on Skill Checks):


  Important: Spending a Clue token always gives you the
  bonus dice that you are entitled to, even if the modifier
  has dropped the number of dice you can roll below 0.