Huder, Ragusa, and Smith have written this article for American Politics Research. Here is the abstract:

Do ballot measures affect congressional voting behavior? Examining the issues of gay marriage, campaign finance, and minimum wage, we test if the results of statewide ballot initiatives inform congressional roll call votes on legislation occupying the same issue space. Theoretically, we expect signals from ballot measures–which provide precise information about the preferences of a member’s voting constituency–reduce policy “shirking” by members. Our findings across the three issues indicate that ballot initiative outcomes alter the floor votes of members of the House, reducing legislative shirking, but we find that the educative effect of ballot measures is attenuated in the Senate due to institutional factors. We attribute the positive effect in House to the precise signal ballot measures provide members about the preferences of the median voter in their district.