On paper it seems reasonable. Space weapons, at least superficially, seem to be a very powerful weapon. Think about it; any low earth orbit takes 90 minutes to orbit the earth. Some politician out there must have done the math and said "WAIT A MINUTE! THAT MEANS THEY CAN HIT ANY POINT ON EARTH IN 90 MINUTES!". His fear grows when he realises that two such weapons cuts the time down to 45 minutes, and 3 down to 30 minutes, and so on.
But then comes the science (alas!). Science says that space nukes are stupid. Not just stupid, but really stupid.
Okay, so you've got your nuke in orbit, going 25,000 miles per hour. Low Earth Orbits have a bad habit of decaying after a few days, months at most. They have to re-boost the ISS every few months to prevent it from falling out of the sky. You'd have to do that to your nukes too; unless you put them in a much higher orbit (ie: tons more money).
Okay, so orbits decay; but! There's another dilly; orbits decay slowly and unpredictably (at least in the case of nuclear weapons, you need accuracy to land these things, right?). So, you need some way of getting that nuke down onto the ground.
You've got two ways to do that.
Way #1 (the hard way): Complete retro braking. You take a huge ass rocket, and when the nuke is over the target, use that rocket to slow the nuke down -25,000mph. Then it will fall onto the target, and kaboom-boom. No spacecraft/sattelite has ever used this method to land on the Earth (though we do it to land on the moon, sort of)
Way #2 (the slightly less hard way): Use a small retro rocket to lower your periapsis (the lowest part of your orbit) to below 100km (62 mi), so that the nuke hits the atmosphere, and uses the atmosphere to slow it down to a reasonable speed, so that it can then land on the target. Of course, you need to remember that the nuke will still hit the atmosphere going about 25,000mph, so you need a massive heat shield to prevent the nuke from being destroyed by the atmosphere.
Okay, so once you get past those problems, you should note that even though sattelites orbit once every 90 minutes, they only orbit over one part of the planet on each pass. Every orbit can be described as a sine wave when plotted onto the planets surface, with the least useful (for weapons) being a flat line about the equator. This is a useless orbit because you could only possibly strike targets along the equator.
So you need a polar orbit; an orbit that goes from north-south over each pole of the planet. These orbits are garanteed to pass over every single point on the planet, eventually. The reason being is that while the nuke is orbiting from pole to pole, the earth is also rotating beneath you, so eventually the target you want to hit will rotate underneath you.
Since each revolution on a polar orbit passes both sides of the earth, you have to wait at most about 12 hours for any point to fall underneath your orbit. Of course, these are coarse measurements, since the earth rotates about 15 degrees per hour. That means that for a 90 minute orbit, each point you pass over will be about 22 degrees away from the point you passed over on the last orbit. For more accuracy, you'll have to wait even longer... (possibly days!) unless...
You use a plane-change maneuver at the equator. Plane changes allow you to change the longitude of the ascending node, which allows you to precisely time where your nuke will fly over... but the problem is that these maneuvers are very expensive in terms of fuel usage. Meaning you have to have another big rocket (or the same rocket with more fuel) up there to aim the damn thing too.
Oh yeah, and there's another catch. Objects in orbit are very easy to calculate the position of. It takes almost no computational power to calculate where an object is going to be at any given time; and it's not that difficult to make a rendesvous with an object in space. That means that anyone can launch a small bomb on a rocket, explode it near your nuke, and all of a sudden it's way off target and probably unusable. Or even better... Say Russia or China gets a vehicle that rendesvous with it, puts it in a payload bay, and then steals it from you?
So, in conclusion, there is absolutely nothing to fear from space-based weapons. ICBM's and SLBM's have proven their effectiveness and efficiency to be far greater than space nukes ever could be.