The easy part is that would take only 1/2 of one chamber. the hard part is forcing a government shutdown is risky business, and maintaining the resolve of the caucus becomes more difficult the longer one drags on.
And whoever's opposed to it can easily spin the action as a reckless disregard for America's security. (Nevermind I think the NSA could disappear tomorrow in a puff of logic and nobody would be the worse..)
