That's a tough one not knowing your field of expertise. Some industries like web design and software coding have no problem dealing with sources outside the US. Other industries simply will not do business with you unless you have a US address.
This has very little to do with your qualifications and everything to do with corporate norms. Let's say you bump into a manager at a gathering that could obviously use your services and personality-wise it seems like a good match. That manager would have to submit your invoice to the purchasing department that simply might not have the ability to process an offshore bill. It may create more headaches than it is worth to them.
Another consideration is the nature of consulting itself. Most consultants are hired in the US not to access their knowledge of a particular field, but to provide 3rd party proof of an already accepted position. Say Company A wants to make a major purchase and their inhouse experts have already crunched the numbers. Before they can present the plan to the Board they require 3rd party confirmation first. So they hire a consultant to prepare a paper on the subject for which they already know the answer. And that 3rd party proof will stand much less chance of rejection if it comes from another US based company.
By the way, that is the trick to being a "good" consultant. Discover what answer the customer is looking for then prepare a report providing that very same answer.