Do any here work as a consultant

Define consultant. Do they want someone there just to be able to claim they have a surveyor on staff? To use your license?

Be sure you are in responsible charge of the work being done under your license.

I would think that a "consultant" is just there to offer advice and information. In which case, yes, you are running your own business.

And I suppose they want you exclusively, their company being your only client, with a provision in your consulting contract prohibiting you from offering services to competing firms or any other potential clients in need of surveying services.

There wanting you to be an employee, but want you to deal with all your own taxes, insurances, governmental paperwork, paycheck deductions, etc. That way they're hoping they can offer you what looks like a really good rate until you figure out what all of your self employment expenses will be. Once you figure in all that and the time you take to maintain the business end of your "consulting", you'll probably find that your doing just a little better than a chainman. Also, they can fire you at any time for any reason or no reason at all, and do it without all the pesky documentation leading up to it and all that messy paperwork associated with terminating an employee.

Could be that your offer doesn't warrant this level of cynicism. It's just that I've worked for an employer who would do such a thing in just such a manner and with just such motives. I see something like this and I see red flags flying.

In Canada, and presumably elsewhere, the distinction, for official tax purposes:

employee:
Is provided with workspace, equipment, hrs within which to work, and relatively detailed work instructions by employer.

consultant:
Provides own workspace & equipment, decides own hrs within which to work, and is given work goals (not details) by client.

Of course there's often grey areas, but heed Dan's & eapls2708's advice:
Beware of saving them money at your expense.