A lot depends on what your consulting goals are:
- Easier: specialized / boutique consulting firms
- Hard: Tier 2 firms (ZS, IBM, Accenture, etc)
- Hardest: Tier 1 firms (Mckinsey, BCG, Bain, Booz)
Now overlay that with how consulting firms hire:
- Top MBA programs: typically the wheelhouse of tier-1/2 firms depending on which MBA program. This does NOT include online MBAs.
- Professional networking: direct connects at networking events, firm-orgranized Mixers, or you know someone who knows someone who knows someone at a firm, or you have an industry reputation already (famous blog, active following on twitter, etc).
- Direct applications: you apply directly through their web portals (if it exists).
So, given your background, etc, the most likely path for you is networking like crazy, start building a 1:1 relations with current consultants, try to get one of them to refer you. You will have the best chance with boutique firms, BUT given you have a PhD from a top program, you might have a shot at the tier2/1 firms if they have expert-track offers (mckinsey has the subject-matter-expert roles). I'd say if you are sure of doing consulting as a career, you should diversify your approach to focus 70% of your time on boutiques, and 20% on tier2 and 10% on tier1. If you only want to do consulting for MBBs, then start networking hard and find a way to get an interview.