The United States on Monday filed a broad trade case against China at the World Trade Organization, alleging unfair subsidies for exports of cars and auto parts. The case comes at a critical time in the United States presidential campaign, as auto manufacturing states in the upper Midwest like Michigan, Wisconsin and particularly Ohio have turned into crucial battlegrounds. But the case may not make any difference in terms of jobs for many months, as W.T.O. cases typically take a year and a half before a final decision is reached, and sometimes longer.