Now this web service starts every word that user key in the text box.
Then using a timer of 'keyboard inactivity' would be silly, wouldn't it? What if somebody stopped mid-word to think about something for a second, go to the bathroom, turn off the stove, etc?
With this in mind, you might want to rethink the design of the application. Maybe you want to add a submit button? Maybe you want to call the service after a certain number of characters have been entered, maybe after you've captured a certain keystroke (e.g. enter, space, etc).
I think it's a terrible idea to make a server request based on the fact that somebody stopped typing for 1-2 seconds, if you don't know that they're actually finished typing or not.
Also, for interests sake, what kind of application are you trying to make?