Silicon Valley and the Beltway have often been accused of living in bubbles, unfamiliar with and wary of others—especially each other. The enmity stretches back decades to unsuccessful attempts by the federal government to bust up IBM and Microsoft, and recent rumbles to rein in social media companies.

The great disconnect between the two, increasingly exacerbated by the growing political and cultural clout of the tech economy, will be on show next week when leaders from Facebook (ticker: FB) and Twitter (TWTR) testify before...