I agree with the previous posters that $100 or more is what it costs to get a quality reproduction. That said, Fall Creek's "emergency issue" blanket (at just under $60) has been cited as an "acceptable" substitute at authentic events I've attended, and their others would probably pass muster, too.
But we should also note that for most of the war both sides struggled with shortages of decent blankets. The Confederates always had a problem, the Union had problems for at least the first year and a half of the war. One of my favorite General Orders, No. 121 of August 29, 1862, reads in part:
"...As the sudden call for volunteers and militia has exhausted the supply of blankets, fit for military purposes, in the market, and it will take some time to procure by manufacture or importation a sufficient supply, all citizens who may volunteer or be drafted are advised to take with them to the rendezvous, if possible, a good stout woolen blanket. The regulation military blanket is 84 x 66 inches, and weighs five pounds..." The order went on to note that by bringing their own, recruits would save the cost from their clothing allowance. This was $2.95 at the time of the order, but went up to $3.60 in December 1862.
Thus, for at least part of the war, an "authentic" Federal blanket would be any pure wool blanket of about the right size and weight. I found a couple in my mother-in-law's basement that I don't hesitate to take to events.