I recently did a same day in Denver by going to the passport office. I had to schedule an appointment though. I do think you can get around that though, as I went in to just get pages added, but ended up getting a new passport instead. They were able to turn the passport around in about 2-3hrs for me. Dropped it off at 10am and picked up at 2-2:30. I wouldn't expect to get it before then, it seemed that all passports had to be picked up between 2 and 2:30. I've heard similar stories from other passport offices, so my guess is that you'd be in luck.
I'd double check with the timing of the Indian embassy. The passport must be dropped off between 9 and 11am for Visa processing. Many embassys usually require all visa issues to get done during this window. Even with a valid visa, you may need to have this dropped off by 11am. You may get somebody to help you out, but my guess is you'll have an issue getting both items done the same day. I don't know if a Visa company can make things any better for you.
Good Luck and let us know how it goes!