Bitterness and IPAs obviously go together, but I don't think an answer has been provided to your liking nor do I think a bitter mouthfeel is necessary in an IPA. In American IPA is often an abuse of hops, but it can obviously have some fantastic results. It is hop overload, but if it is so bitter that the character of the hops blurs, you failed. Also, it depends on what hops you use. You can make a great IPA with a malty backbone that can swallow up IBUs and leave a product that does not seem bitter at all, but still meet the style guidelines for an American IPA. You need enough bitterness to overcome the sugars obviously, but you can still bomb an IPA with hops and not get bitterness. That is essentially the point of late addition hop bursts and dryhopping, which preserve the volatile oils and flavors without imparting much bitterness. an IPA can be insanely hoppy, yet sweet if you want it to be. I'm currently devising my first recipe for an IPA and my first hop addition is going to be at 10 minutes left in the boil. I will be adding 11 ounces between 10 and 5 minutes left, which should give it enough IBUs to balance as well as a huge hop flavor that does not include overwhelming bitterness. I also plan to dryhop. Obviously, this recipe with 14 ouces for a 10 gallon batch may not be economical for everyone. However, there is a method of hopping called first wort hopping that can help add a perferable hop complexity to you beer. This is when you add hops to the kettle at first runnings and let them soak in the warm wort during sparging. This allows the hop oils time to oxidize to more soluble compounds, which helps preserve them throughout the boil. This is a great way to get a bit of flavor from your bittering hops. If you want a real balance that has a clean malt and hop presence, I would recommend a Czech pilsner. Pilsner Urquell is very pleasant.