I live clear over in Portland, but I visit eastern Oregon a lot (and that area in particular). My impression of the people in Burns and thereabouts is that while most are pretty conservative in their politics, they are not anti-government, teahadist extremists at all. A large percentage make their living from the federal presence in the county (either working for the BLM/Forest Service or providing goods and services. They are fairly typical small town folk (or at least the oddball Oregon version thereof) who will NOT be amused at out-of-area dickheads with guns and an agenda invading their town. They might have their issues with the BLM (who can be high-handed, to say the least), but they're inclined to settle matters with the ballot box, not the cartridge box...just like sane people everywhere.
I don't envy Sheriff Ward. When the militants first seized the refuge compound, there's no way he would have had the manpower to try and stop them. Harney County has not much over 7000 people total (in a county bigger than seven US states); there's no reason to have a large sheriff's department, and the only town with a police force of its own only has it because it's tribal land. Ward was dealing with a potentially violent group that outnumbered the forces he had available (although I think if the teahadists had started anything, Ward would have had scores of locals willing to help defend their town...but what an unholy bloody mess that might have turned into).
By tomorrow morning, I suspect there will be a LOT of law enforcement there, including possibly an FBI weapons team, given that they've seized federal land. I expect a patient solution (a siege is preferable to bloodshed), but if it really does come to a fight, the advantage will be on the side of the law.