Oddly enough, I have thought about this a bit. 
I came up with a couple of lists that, in theory, could work really well. I think the majority of marine players that want to go assaulty tend to gravitate toward BA, SW, or BT since they've all got an edge when it comes to assaulting power armor (or just go to the dark side since Chaos can do it even better).
My ideas revolved around what you'd need to have to get the job done:
- A way to keep your assault units relatively safe until they hit combat.
- A way to deal with things that typically hurt assault based armies the most (things like tanks, skimmers, etc... ).
I ended up with two, fairly similar lists - both of which I like a lot but neither of which I'll be capable of building any time soon.
List 1
Jump Reclusiarch or Codicier w/Fear
x5, 6-man Assault squads
x3, 6-man Tac squads (all with dual meltaguns and in Drop Pods)
x3 Pred Destructors
Basic Idea: Run the assault squads behind cover and a wall of AV 13 goodness until close enough to jump out and pounce. The Pods either hit things in the backfield that will give you fits, or add even more cover for you to use as you work your way forward. Why Preds and not Vindicators? Well, the Preds are the cheapest way to get yourself some good cover and help out with the skimmer issue to boot.
List 2
Jump Reclusiarch or Codicier w/Fear
x2, 8- man Assault squads
x2, 8-man Tac squads in Rhinos
x4, 5-6 man Tac squads with dual specials (either meltas or plasma) in Pods
x2 Pred Destructors
Basic Idea: Very similar concept. The Rhino squads would be kitted out for assault as well, allowing you to dump them out the turn the Assault squads hit and then pile in the following turn to mop up. You're more dependant on your vehicles surviving since only 1/2 your assaulters have jump packs on, feels a litte more tricky to use than the previous list.
So yeah, I think it's a viable idea if you tool your army for it.
Kev