The New Republic is probably the best candidate for "magazine representing the center of American politics." It was founded by people loosely affiliated with the Democrats, and it does continue to generally favor Democrats, but invariably Clinton-type neoliberals; at the time of its founding, a major part of its focus was on formulating the Left's response to Stalinism, and defusing the right-wing's jingoistic claims to being the only people capable of fighting communism. As a result TNR has always been suspicious towards socialism, even of the more benign Swedish variety. It quite regularly offers column inches to libertarian and conservative people; they gave Greg Mankiw a multi-page article in which to lay out the case for privatization (which Brad DeLong promptly eviscerated). When it tilts right, it's often cited by conservative pundits as "Even-the-liberal-New-Republic" (as in "even the liberal New Republic has come out in favor of the Iraq War" -- yeah, they were snookered by Colin Powell, and had always favored regime change; they've since kinda-sorta admitted that maybe they shouldn't have supported the war, given the known incompetence of the current C-in-C). TNR's worst trait, historically, has been an unhealthy committment to Zionism in the non-pejorative sense (simply believing that Israel has a sovereign right to act to maintain itself as a uniquely Jewish state, and that Israel is a valuable American ally), to the point that they often listed over into the bad kind of Zionism (privileging Israeli Jews' human rights over Palestinians' human rights).
So, understanding this history, it's shocking to see this week's issue fully endorsing the Gaza pullout (and slamming the resistant settlers: "The settlers of the West Bank and Gaza are not a Jewish vanguard, they are a Jewish sect; and in their insistence that the destiny of their state and their society should be held hostage to the fulfillment of their metaphysical and historical conceptions, they have always displayed a sectarian self-love."), and according Cindy Sheehan some respect. They also take some brief swipes at the Republican war on science and Pat Robertson's call for a political assassination ("[T]he U.S. struggle against violent religious extremists abroad is damaged significantly when our own religious extremists all too casually resort to violent exhortations."). They also have one of the best analyses of California politics I've seen, particularly on the role of Props 13 (our screwy property tax system) and 140 (legislative term limits) in destroying California's history of successful consensus between libertarians and progressives.
Could it be that they're tracking the center back towards a sane assessment of the Republican agenda?