Well, you've "been asked" to do it.. employment is always "at will" ;).

Assuming you are an exempt worker (non-hourly), they obviously don't have to pay you for overtime, but you do have to be off a "full week" for a furlough week to count. If you do any work during the furlough week you will have to be paid, as far as I know.

You might want to check your employment contract or employee handbook and see if there are clauses about what they expect from a "typical workweek" or anything like that. Otherwise I don't think it is necessarily illegal. You can always call your state or federal Department of Labor and ask, or take it up with your company's HR department. Though if I were you I would fervently seek other opportunities ;).