According to a new working paper, the answer is no -- not by a long shot.
A working paper by political-science graduate students David Broockman of Berkeley and Christopher Skovron of the University of Michigan suggests that there's an effective supermajority requirement for passing liberal bills within state legislatures because those lawmakers routinely overestimate the conservatism of their constituents.
Their paper, "What Politicians Believe About Their Constituents: Asymmetric Misperceptions and Prospects for Constituency Control," found that "[T]here is a striking conservative bias in politicians' perceptions, particularly among conservatives: conservative politicians systematically believe their constituents are more conservative than they actually are by more than 20 percentage points on average, and liberal politicians also typically overestimate their constituents' conservatism by several percentage points."
The survey studied opinions of nearly 2,000 state legislative candidates and compared it with "actual district-level opinion" based on other surveys.
Dylan Matthews dug into some of their data over at Wonkblog, concluding, "The graphs show that the threshold of support a liberal policy must cross for politicians to back it is well above 50 percent, and above 60 percent for universal health care. If only 55 percent of a district supported universal health care, then more likely than not, their representative will oppose it."