Ajax Request To SQL Server Opens Too Many Pooled Connections?

I'm implementing a Google like search box in my asp.net application. Each keypress in the box sends an Ajax request to IIS webmethod that queries the txt and return matches - works pretty cool. However, on loading up activity (e.g. 300 users), I'm getting errors that my 100 Pooled connections are used up. Now I'm rethinking that perhaps opening/closing a db connection on each keystroke may be too much. How would one architect this differently, or insure that the connections are reclaimed really fast. I'm have the 'using' construct for connections to insure it is closed. The concern is GC may not be reclaiming them fast enough?

How would google handle such a large open/close cycle.