'Officially', Dee Sa's statement that 'minor offences don't count' is incorrect. The US embassy website states that anyone who's ever been arrested (even if totally innocent) or convicted of any offence is ineligible to use the Visa Waiver Program. (The only exception is for minor, non-arrestable, motoring offences, such as speeding). See SpudQueen's link for further information.
However, as Bednobs states, obtaining a US visa usually takes longer than 3 months. (Typically around 5 or 6 months). Anyway, we don't know that you're not a model citizen, with no brushes with the law.
Irrespective of whether they've been arrested or convicted, thousands of people enter the USA by simply filling in the form on the plane. (The US authorities have no direct access to UK criminal records). However, anyone who answers 'Yes' to the question about arrests and convictions will automatically be turned back by immigration staff, because they've admitted their ineligibility to use the Visa Waiver Program.
Chris