On the left, identity plays a crucial role in political activism and their activist groups are often organized in such a way to bring attention to this fact. Whether they be African American, Chicano, gay, or otherwise, peoples grievances are usually anchored to some aspect of their identity.
Even at rallies that wouldn't at first glance lend themselves to identity politics, it's common to see placards that identify the protesters as a member of some group. Anti-war protests for example are always peppered with signs that declare membership to socialist workers groups, Hispanic organizations like la Raza, or women's groups like NOW.
Seeing as the left finds its identity in the group dynamic, it stands to reason that they'd looking to anchor their opposition to identity as well. To this end, in vilifying the tea party movement, they simply chose the most shallow and politically damaging accusation; intentional, and exclusionary whiteness.
It should be remembered that before the left settled on their race narrative, they were still attempting to marginalize the tea party with identity. In the movements formative days, politicians and their spokespeople tried to paint protesters with a broad socio-economic brush. For example, Whitehouse Spokesman Robert Gibbs took to calling town hall protesters as the "Brooks Brothers" mob, while Speaker of the House Nancy Pelosi insisted that they were little more than astro-turfers, obviously paid for by some nefarious healthcare cartel.
Despite these attempts at marginalization, the rapid growth and continued mobilization of thousands of Americans quickly rendered this narrative absurd on its face. The facts did not bear out their accusations and the people simply weren't buying it. Instead, it would be necessary to pull out the old stand-by; race.