It's a cop-out. A massive ducking of responsibiltiy to yourself, your environment, the future of your progeny... That's what crystalized for me the moment I read the title, a white-hot point of anger and frustration that makes me want to beat my head bloody on the nearest flat surface.
Setting aside the fact that if there is going to be an end to the earth as we know it, the human race is perfectly capable of destroying itself in fire and ice without divine help or intervention, let's examine some of the more problematic aspects of this notion. First of all, what makes you so special? Meaning various peoples, sects, prophets and so forth throughout the ages (pre- and post-christian) have been possessed of the idea that they were living in the "end times." Guess what? They died, and that's all the 'end times' there were. The universe continued, and here we are today. How bloody arrogant to assume that your personal feeling of impending doom forecasts the cessation of anything other than your personal self! So here we go again, now Mr. LaHaye thinks it's the 'end times' - but of course he's not like all the others, historically - he's right. *nods sagaciously* Now, maybe he's one of the ones who figure that times didn't end in the past because people straightened up and flew right, but I'm dubious.
What really irritates me, though, is how 'these are the end times' flows so easily into 'so we don't have to worry about the future'. Pollution, over-population, diminishing resources? These are the End Times, so 1) of course things are going to be nasty - preferably Somewhere Else, so we can read about it comfortably and speculate on how it answers prophecy rather than actually experience it ourselves and 2) but hey, it's ok because soon it will All Be Over - we'll just sit tight and things will take care of themselves.
It's the externalization of the very selfish notion of short-term gains over long-term detriment. That bumper-sticker about "I'm spending my grandchildren's inheritance" is a truer saw than many. Why build something to last? It's the End Times - a stop-gap will do, until the New Heaven and Earth. (Which, I suspect, will look suspiciously like the Old Heaven and Earth except older.) How many New World Orders do we have to sit through before people figure it out? And you know, even if somehow this particular vision of now being the End Times happens to be right - why should that change your behavior? Isn't it a better idea to live with a care for the future, just in terms of quality of life?
The earth will abide - I can't speak for the heavens, being less than well aquainted with those environs. But the earth was here before us, and one way or another it will be here when we are gone - for any definintion you want to slap on the instance of "we". The world goes on when you shut your eyes - why should it be any different when you are dead? Even if you were the person who pushed the button that vaporized the planet, the vapor remains, the dust remains, the earth remains - the only thing that ends is you, and as ego-devistating as it may be to contemplate, that rates a big old "so what?" as far as the mechanics of the universe go.
See, as far as I'm concerned, if there is anything particularly noble about the human race, it is our continuing to behave as though what we do matters in spite of all the evidence to the contrary. That's a big "if", but there it is. Calling it the End Times and expecting that to serve as an excuse for lack of care for the future undermines that, and irresponsibly so. And who is going to suffer, in the future, when the Times don't End and the consequences of these people's short-timer shortsightedness come to fruition? Well, that's where I get cranky, because it's not likely to be the shortsighted ones themselves.
None of this even begins to address fear of change, either. Another facet for another day - or you can go read Octavia Butler's Parable of the Sower and Parable of the Talents where she discusses such things better than I.