Disclaimer. Don't rely on these old notes in lieu of reading the literature, but they can jog your memory. As a grad student long ago, my peers and I collaborated to write and exchange summaries of political science research. I posted them to a wiki-style website. "Wikisum" is now dead but archived here. I cannot vouch for these notes' accuracy, nor can I say who wrote them.
Hetherington. 1999. The effect of political trust on the presidential vote, 1968-96. APSR 93:311-26.
Declining political trust (see Fig 1) has not affected turnout, but it has affected vote choice. When there are two parties running (viable) candidates for president, distrustful voters turn to challengers (not incumbents); when there are three candidates, distrustful voters turn to third parties.
Trust in government can serve as a heuristic (info shortcut). With candidates frequently running anti-Washington campaigns, and the media constantly pointing out government waste, distrust turns into a convenient heursitic; as a result, presidential voting represents a clear tendency among the distrustful to "turn the rascals out."
Using NES data from 1968-1996, the author shows that distrust predicts individual-level voting against the incumbent (in two-party races) and against the major parties (when there is a strong third-party candidate). If trust had remained at 1964 levels, incumbents would have fared slightly better (Table 5), though probably not enough to have won reelection if they lost.
Research on similar subjects