Obviously, calling a group 'irrelevant' can simply be the harshest sort of swipe. And in a sense it is. But I mean it more specifically. During the 1980s and 1990s, the Democratic Leadership Council (which, not coincidentally, went out of business two years ago), definitely had a constituency in right-leaning Democrats from the South and Midwest. It had a policy-political constituency in the widespread belief that the national Democratic party had discredited with the public on issues like national security, welfare, crime, etc.
There's no point in rehearsing the discussion of whether that was accurate or not: it was the baseline question around which a lot of campaigns and policy debates were argued during that period. The Democrats did lose 5 out of 6 consecutive national elections (1968-1988). And its one-time Southern base appeared to be (and was) in permanent decline.
It is fascinating to remember that one of the high profile 'victims' of the 1994 Republican landslide was David McCurdy, then a member of the House trying to make his jump to the Senate and a man very much with national political ambitions. And he was from Oklahoma. It's hard to imagine any Democrat trying to build a national political career from Oklahoma today.
Things look very different now. Republicans have won the popular vote only once since 1992 and a fairly progressive Democratic President was just reelected during a period of slow growth and high unemployment. It's just hard to make any credible argument that the Democratic party, either objectively or subjectively, has drifted outside the mainstream of American political life. Nor is it easy to argue that both parties are captive to their extremes and a 'third way' is necessary. Certainly, it's hard to make that case to Democrats, whereas there was a decent constituency of Democrats who very much did believe that twenty and thirty years ago.
The key policy question facing Democrats today is whether there is any credible or viable policy prescription to arrest the trend toward a winner take all society in which the top 10% or 15% do better and better and the rest stagnate or lose ground. In other words, the question of the day is inequality and whether we can act collectively to do anything about it. In that context, cutting taxes for high-income earners and retrenching social insurance programs like Social Security and Medicare is a pretty tough sell.
Back during the time he was in the House and angling for promotion to the Senate, Harold Ford used to say, "I didn't leave my party; my party left me." Of course, that's an old line told by countless Democrats in the post-60s era. But it perfectly captured Ford's ridiculousness in the post-Clinton era since for most people who used to say that, the time when the Democratic party 'left them' was in the 60s or early 70s. That is to say, around the time Ford was born.
That captures a lot of what the 'Third Way' is about: a sort of fossilized throwback to a period in the late 20th century when there was a market for groups trying to pull the Democrats 'back to the center and away from the ideological extreme' in an era when Democrats are the fairly non-ideological party and have a pretty decent record of winning elections in which most people vote.