My experience is that going to the visa section of any country in person and stating simply that you need a visa within "x" days (provided "x" is not unreasonable - like demanding a visa for travel the next morning) will usually get you the visa as quick as possible. Indian visas CAN be processed overnight, so asking for next day service is not a stretch. Offering to pay a "surcharge" (official or unofficial) also helps sometimes. Look up the name of the Head of Visa Section ("First Secretary - Consular" might be the title) and ask to speak to them directly - you probably won't get that far but name dropping ALWAYS helps.