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."
What that means is that the supermajority requirement for support that is the new normal in our national legislature for (many, though not all) liberal bills to pass also exists at the state legislative level.
The study authors don't really get into why. But here's one theory: The overall political views of a district are less important for policymaking than the organized political groups in a district, and conservatives have since the 1970s pursued a strategy of robust organizing within states in the service of pushing conservative policies. In recent years, anti-abortion groups in particular have worked to lobby state legislators, vastly outstripping abortion-rights groups on the ground in state after state and creating a powerful constituency for change in a socially conservative direction.
Matthews says the data show that "epistemic closure on the right is real," but I don't think it's that conservatives are out of touch with their constituents and unwilling to listen to others, so much as as that they are in touch with a highly organized infrastructure of pressure groups dedicated to lobbying them to vote even more conservatively than their overall constituency might wish. Liberals have never been able to (or, more commonly, sought to) match the extent of state-by-state organizing and statehouse lobbying of conservative groups and causes, even though comparatively small investments can reap major rewards in such environments.