Since Citizens United v. Federal Election Commission was decided in January 2010, several polls have shown the decision is unpopular. A Washington Post-ABC News poll taken a few weeks after the decision found that nearly 80 percent of respondents opposed it.

Unsurprisingly, many politicians have reacted to these numbers like cats to catnip. Recently, a Senate Judiciary subcommittee held hearings to consider reversing it by amending the First Amendment to the U.S. Constitution.

Senators should tread carefully, though. A fuller reading of polling data casts serious doubt on whether such an amendment would really be popular.

Two years after Citizens United, the Democratic pollster Greenberg Quinlan Rosner asked a series of wildly biased questions to prime the pump against Citizens United. Respondents were asked if they agreed with statements like:

á "I am fed up with the big donors and secret money that control which candidates we hear about. It undermines democracy;"

á "There is too much big money spent on political campaigns and elections today and reasonable limits should be placed on campaign contributions and spending;"

á "The middle class won't catch a break unless we start by reducing the influence of big banks, big donors and corporate lobbyists."

Even with such pump-priming, however, only 62 percent opposed Citizens United. That's a sharp drop from the 80 percent in the 2010 Post poll, but still a large majority, even for a push-poll.

But both the Post and the Greenberg Quinlan polls left out a crucial question: What did voters really know about Citizens United?

Past polling has shown immense public ignorance of campaign finance laws. In January 2012, my group, the Center for Competitive Politics, commissioned a poll that found 76 percent of respondents still did not know that "super PACs" must publicly disclose their donors.

We had also commissioned a poll of likely voters in 2010, just weeks after Citizens United was decided. We asked, "Are you aware of or have you followed the recent Citizens United case, related to corporate and union spending in elections, decided by the Supreme Court last month?" Only 22 percent answered yes, while 60 percent said no and 18 percent were unsure or refused to answer.

We then asked respondents about the actual issues in the case. When asked, "Do you believe that the government should have been able to prevent Citizens United, an incorporated nonprofit advocacy group, from airing ads promoting its movie?," 51 percent of respondents agreed with the ruling and only 17 percent disagreed. When we asked, "Do you believe that the government should have been able to prevent Citizens United ... from making its movie available through video-on-demand technology?" we got a nearly identical result.

Finally, we asked voters directly about the core question of Constitutional interpretation in Citizens United: "Do you think that the government should have the power to limit how much some people speak about politics in order to enhance the voices of others?" By nearly four to one, respondents, like the court, said no.

These findings are consistent with deep public support for the Supreme Court's long-standing holding that campaign contributions and expenditures are vital to free speech protected by the First Amendment.

Polling data on campaign finance has always been extremely sensitive to wording, and the public is historically inconsistent in its preferences. In a study of years of polling data, political scientist David Primo, of the University of Rochester, concluded that on any close examination, the public's views on the subject are "wishy-washy," and reflect "a tension between freedom of expression and a desire to prevent corruption."

An actual proposal to amend the First Amendment would force voters and legislators to face the problems of regulating political speech. If that happens, politicians who jump now to support it might find themselves on the defensive.

Bradley A. Smith is co-founder and chairman of the Center for Competitive Politics.