Current information on this project can be found on http://map.wyoroad.info/hi.html
Note the phone number provided, 307-200-9188. They actually called us back.
In mid August 2014 we did this (southbound) by arriving at the construction at 5pm and riding until dark, then rising early to get through the rest. In most of the 27 miles the surface was adequate to good. The closure barriers were not up when we passed, but it appeared that the southermost 8 miles were the actual closure area.
We have heard of angry workers and conflicts from other travelers trying to cross this, but we had no trouble, nor did another couple on the same day.
If I had it to do again I'd just do the suggested reroute if only because of the length of the construction zone.
Here is a copy/paste from today's info on wyoroad.info:
WY 71 Sage Creek Road
Project Number: WY PFH 26-1(3)
Scheduled Completion Date: 2015-Jan-01
WY 71 (Sage Creek Road) has construction starting Monday May 12, 2014. The road will be CLOSED to vehicles Monday-Saturday 8am-12pm and 1pm-5pm excluding federal holidays. If you need accommodations call 307-200-9188. construction expected to last 6-7 months.
Road Milepost(s) Surface Delays and Scheduled Closures
US26 26.0 to 34.53 Gravel, Dirt
Closed, on -MTWTFS, from 1300, to 1700
Closed, on -MTWTFS, from 0800, to 1200
Last Updated: 2014-06-25 00:17:52.428