I have read books where authors deliberately misspelled words to try to describe the character's speaking. However, I personally think that this makes it difficult to read and awkward.
Instead of focusing on how the character mispronounces words, think about the rate at which the person speaks. That's something easier to get across.
"Wha... What am... I..." He stumbled across the floor and flopped onto a chair. "What am..." He closed his eyes as if the words were just too difficult to force out of his own mouth. Finally, mustering together all of his strength, he finally managed to croak out, "I... doing here?"