Every day there is a headline or feature on the Lieberman-Lamont primary contest in Connecticut, today's being that Lamont is in a dead heat with the incumbent, and that Bill Clinton has come to town to declare for Lieberman.

Here are thoughts for independent voters to consider, even if they don't speak these thoughts out loud.

(l) Conservative voters don't have very much to applaud in Lieberman. Yes, he has been faithful to his word in supporting the Iraq war. But his conservative impulses live very short lives. For a photogenic moment, he turned on Bill Clinton after the Lewinsky episode, registering dismay over what Clinton had been up to. The most decisive means for a Democratic senator to register that dismay was to vote to affirm the impeachment of Clinton. But Lieberman didn't do that. When the big moment came, he voted against conviction. Bill Clinton has now affirmed his own support for Lieberman by traveling to Connecticut to back him in the primary fight.

Lieberman intuitively questioned the implications of affirmative action. But when the vote came, he voted against the principles he had adumbrated. Lieberman sensed the strong case for school choice. But -- yes: When the time came, he opposed choice (although he has since supported school vouchers in Washington, D.C.). He opposes a constitutional amendment to ban same-sex marriage, opposes the ban on partial-birth abortions, voted against Samuel Alito for the Supreme Court, voted against drilling in the Arctic preserve -- and so on, earning a zero from the American Conservative Union.

(2) Conservatives can't, under the circumstances, make ideological headway by voting for Joe. But what will happen on Aug. 8 is enormously important nationwide for the future of the Democratic Party. The backing for Ned Lamont is by people, explicitly and implicitly, who wish to send the Democratic Party into a hard left turn. They are the equivalent of the Henry Wallaceites in 1948.

Wallace, having been rejected for renomination as vice president by FDR, turned against Harry Truman, his replacement, and bade for command of the Democratic Party. The Nedheads (as they are being designated) want to try that in 2006. For Wallace, the cardinal question was how to deal with the Soviet Union. For the Nedheads, it is how most deeply to reject the memory of George W. Bush and his works.

(3) The turnout in Connecticut primaries is pretty small, traditionally about 20 percent. This year the Democratic turnout will be larger, that primary being the focus of national interest and the harbinger of the future ideological cast of the Democratic Party.

Now here is a furtive thought. Everybody is concerned with what happens in Connecticut on Aug. 8, but only voters registered as Democrats can have a say in the matter.

Forty-nine percent of Connecticut's voters are unaffiliated-unregistered in the national parties. However, I (a Connecticut unaffiliated voter) could sign up as a Democrat as late as Aug. 7 and vote in the primary the next day. Christians trained in the Catholic discipline would think of such a sinful act as a lapsed moment, rather than as a defection -- on the order of a night out, as distinguished from a divorce. If a Connecticut conservative were spotted in flagrante emerging from the Democratic primary booth, he could plead that he was heeding calls to protect his country's future. He could even say, after catching his breath, "Hey. What is this? Iraq?"

If Mr. Lieberman is defeated in the primary, he will proceed to run as a "petitioning Democrat." Only a single name can be listed under the simple designation "Democrat." What we would then see, in November, is how Connecticut voters at large feel on the question of Lieberman, a three-term Democratic senator, over against Lieberman as Democratic reject, but alive as a "petitioning Democrat."

It is required, at this point, to note that the Republicans do have a candidate. His name is Alan Schlesinger. And if the New Democrats and the Revival Democrats have a bloody and internecine contest, the result could be ... a Republican senator from Connecticut! That was the chance Connecticut voters missed 26 years ago when they rejected the Republican candidate, who had for six years in the 1970s been acknowledged as the Sainted Junior Senator from New York, James L. Buckley.