POLL: Trust on Issues: Voters Give GOP First-Time Lead on Health Care. “Democrats held a four-point lead on the issue last month and a 10-point lead in June. For most of the past two years, more than 50% of voters said they trusted Democrats on health care. The latest results mark the lowest level of support measured for the party on the now-contentious issue.” It’s not that the Republicans are doing well; it’s that the Obama Administration is doing badly.