Vincent Racaniello from This Week in Virology has a great post on his site about what happens to the immune system during the initial infection of an influenza virus:
During the earliest stages of a virus infection, cytokines are produced when innate immune defenses are activated. The rapid release of cytokines at the site of infection initiates new responses with far-reaching consequences that include inflammation.
One of the earliest cytokines produced is tumor necrosis factor alpha (TNF-α), which is synthesized by activated monocytes and macrophages. This cytokine changes nearby capillaries so that circulating white blood cells can be easily brought to the site of infection. TNF-α can also bind to receptors on infected cells and induce an antiviral response. Within seconds, a series of signals is initiated that leads to cell death, an attempt to prevent the spread of infection.