So I was trying to renew my wife's passport. After 3 weeks without a response, I tried calling. After redialing several times, I got into the voicemail. But I must say it's one of the toughest puzzles I've ever solved. It's a virtual maze that takes you in mind numbing loops and leave you with no chance of ever getting out.
So all you guys searching the web for the magic extension - it's “138″ and it takes you right to a polite person who can answer your question in 30 secs. Also try email for a same day response.
But why they still use this completely unusable voicemail is a mystery. Probably they're trying to keep away aggressive callers used to calling unresponsive government offices in India.