Very much agreed with the majority. 1 milestone is a "6 minute day" style -- and isn't what 4e is meant for. LFR is a bit too easy with 2-3 combats per mod and 1-2 skill challenges; real campaigns tend to go at least 2-3 milestones per day to keep the PCs honest.
There are plenty of ways to do this. You can design your adventures as stories, not dungeons--once the story begins, they can rest only by losing whatever the story is about; there is a ritual that's about to go off/a race for a mcGuffin that they'll lose/a prisoner that'll get sold into slavery/an innocent woman hanged for murder. This is classic -- and makes sure that PCs have a reason not to rest. If you want to make things more interesting, you could even give a multi day time limit and make sure they have enough things to do that this isn't trivial -- with some internal goals that need to be handled on the spot.
If you really need to run a dungeon (or any assault scenario, really), make sure your dungeon is alive. Sure, the encounters in the dungeon need to be disconnected enough that PCs don't end up fighting the entire dungeon at once and dying horribly -- but that doesn't mean that if they take out a room or two and retreat, that they won't have a nasty surprise waiting for them when they return--maybe they'll find a huge ambush waiting...or maybe they'll find the formerly rich dungeon an empty husk, as the denizens have heard the scent of adventurers and decided to move to safer pastures. Once the PCs start to assault an area; whether it's a dungeon, a castle, or anything else, make sure they rarely have more than a day to finish the job.
If the idea of actualy running stories (or rather, situations) bugs you, there's a more radical possiblity too. Get rid of extended rests (and even short rests) as a tactial option entirely. The PCs get the benefit of a short rest when you say so; maybe the neeed to travel quickly means they don't get a short rest when they'd like one--but when a battle extends into a giant melee, they find the surge of adreniline raising their spirits (and giving them their encounter powers back, letting them spend healing surges, etc). They get the benefit of an extended rest when you say so too -- maybe in your universe, sleep isn't enough; instead one must take advantage of healing pools -- or brief trips to the realm of the gods -- or just moments of utter peace--things you can't expect to come back to later and still find the same, to restore their health and recharge their daily powers. That way, the extended rest isn't a tactical decision on their part; it's a feature of the encoutnter, and the question isn't "we've hit too encounters and burned through our dailies/surges because we don't believe in saving resources, should we rest now?" but "ok, which of these three paths leads to another enchanted pool--because I'm pretty much down to encounter powers and at-wills.