I think we can all agree (and Mike and Rodney seemed to also) that creating a "tactical system" within the Fighter's Maneuvers is easy-peasy. Creating a "Fighter Tactician" won't be any real issue as they design it, and thus that one half of the 4E Warlord can be covered without any problem. It won't have the class name "Warlord"... but the character would pretty much be just that. And I would suspect that that's probably not going to be a real issue for most people. Because the "tactics" and "buffing" aspects of the Warlord are not what cause the most consternation.
Thus, we come back to the real issue... which is healing. And the question which is "How much ingrained healing ability (flavored as inspiration) does a class have to have to warrant having its own class?" That's the issue. Because Mike was right... you could easily take the Fighter with one of the "tactical" maneuver builds and then select the Healer specialty, to get most of the abilities of the Warlord. But is the Healer specialty enough for many 4E players? I'm willing to bet that... No... they are going to want a fuller suite of "healing-like" abilities above and beyond a simple Specialty. Which I can certainly understand... because it mimics the argument of whether you need a Paladin class when you can make a Fighter/Cleric, or whether you need a Ranger class when you can make a Fighter or Rogue with an outdoorsy Background?
I feel like you get right to the heart of the argument.
The "tactical fighter" is a common archetype. Having it in the game just makes sense. Now whether that comes about because of fighter options or a new class is the mechanical question. I personally would rather have it rolled in to the fighter because I think it gives more flexible options (I can dip into the tactical without going full in having to take another class). I was a big fan of the Warblade 3.5 class for this reason, I felt like I slide stats into more int and gain different fighter benefits. But either way works.
Now we get to the "thorny" issue. Should healing occur without magic? Looking on these boards alone, I think the core answer is....no. Healing seems to be an incredibly divisive issue in the community, and no matter how we flavor or dress it up, allowing non-magical healing to be on par with magic is just not going to fly.
But I don't think its the end of the story. I think there is a place for the non-magical means of "resisting death", which ultimately is what HPs are all about. A warlord could provide "temporary hp", a "second wind" mechanic, "damage reduction", "increased death's door mechanic", "increased HD regeneration", etc. As long as the effect is different from magic, and most likely will need to be weaker, than I think the community could accept it.