Wolverine might be the best at what he does (and what he does isn't very nice), but he's not nearly as indestructible as his reputation has led people to believe.
In fact, that healing factor has let him down a fair few times over the years, and while you'd think an adamantium skeleton would, presumably, go a long way in averting death, what was once a powerful asset has become a weakness on more than one occasion. This means that Logan - old man or otherwise - has racked up a bunch of deaths in the comics over the years, some administered by rudimentary methods, while others have taken a more... creative approach.
And that's not to say that Wolverine doesn't live up to his reputation; he's one of the deadliest mutants in the biz, and with that healing factor to help, it makes the prospect of genuinely killing him a tricky one to contemplate. It's not unfeasible (the character was, until recently, deceased in Marvel's main 616 continuity), but going about stopping Canada's preeminent comic book character is a lot easier said than done. (The Hulk, incredible though he may be, knows this better than most.)
It's the murder plot to end all murder plots, but put into practice correctly, and the X-Men could be in a whole lot of trouble.