"There are about 45 million acres of public rangelands in Nevada. These rangelands are divided into 745 grazing allotments. There are 550 operators, or permittees, with a total of 635 permits to graze livestock."
https://www.blm.gov/nv/st/en/prog/grazing.html
This page says the total acreage of BLM land in Nevada is about 48 million:
https://www.wildlandfire.com/docs/2007/western-states-data-public-land.htm
So, the answer to your question is "no". There appears to be plenty of government rangeland available to ranchers in Nevada.
The total acreage of BLM land set aside as "wilderness" in Nevada is 2,056,545. That is about 4%. Another 2.5 million-or-so acres is designated as a "wilderness study area". I guess that may or may not eventually become "wilderness", but is probably managed currently as "wilderness".
To summarize:
* About 90% of BLM land in Nevada (significantly more than 50% of the state) is public rangeland.
* About 8% of BLM land in Nevada is currently managed as wilderness (around 5% of the total land in the state).
Thanks for agreeing.