Brimley is the first to figure out what's going on because he asks his computer, and it's a computer in an '80s movie, so it knows everything. The computer also tells him that if this alien crap gets to civilization, all human life will be gone in about three years, which would put an unacceptable dent in sales of Quaker Oats. So Wilford does what any pudgy fella in suspenders and an old-timey nightshirt would do in this situation -- he picks up an axe and gets to swingin'. And yellin'. And mumblin'. And swingin'. He wrecks their helicopter, kills a bunch of dogs, then goes after the radio equipment. The thing is, even though he seems like Santa on a drunken tear, he's actually trying to save the human race by making sure that none of the potentially infected people on base ever gets out alive. He knew what was up. You can see why he became so smug and condescending about stuff like oats and Liberty Medical supplies after this..
Final stages of "Diabeetus." He tried to warn us.
The other men can't contain Wilford's raw power. They send Keith David to talk to him, probably because of David's silky smooth baritone, but that just makes him angrier. He drops the axe and pulls a pistol, throwing out an "I'll kill you!" that'd make Yosemite Sam blush. Eventually it comes down to Kurt Russell and three other guys taking him down WWE-style: with tables, chair-hits to the face, the whole nine. They finally knock him out and lock him up. But, despite having the oldest-sounding-name in recorded history, Wilford Brimley's still not through. Turns out he was infected (theories about when this could've happened abound on the Internet, and are absolutely NOT worth your time) and he transforms into a hideous giant monster and ultimately gets blown up with dynamite. Weirdly, Wilford's character in The Natural met the exact same fate.