The atmosphere rotates along with the Earth for the same reason you do.
Force isn't needed to make something go. That's a basic law of physics - that a thing that's moving will just keep moving if there's no force on it.
Force is needed either to make something change its speed, or to make its motion point in a new direction. A force can do both or just one of these. Most forces do both, but a force that pushes in the exactly the same direction you're already going only changes your speed, and does not change your direction. A force that pushes at a right angle to the direction you're already going only changes your direction, and does not add any speed. A force at "10 o'clock", for example, will change both your speed and your direction.
As you stand still on Earth, you continue going the same speed, but your direction changes; between day and night you move opposite directions. So the forces on you must be at a right angle to your direction of motion. Indeed, they are. Your motion is from west to east along the surface of the Earth, and the force of gravity pulls you down towards the center of the Earth - the force and your motion are at right angles. Similarly for the atmosphere. It is moving along with the Earth, and moving at a constant speed. It does not need anything to push it along with the Earth. Since only its direction of motion is changing, it only needs a force at a right angle to its motion, the same as you, and the force that does the job is again gravity.
That's not the whole picture, because the amount that your direction of motion changes depends on how strong the right-angle force is. It turns out gravity is much too strong for how much our direction of motion changes as the Earth spins. There must be some other force on us and on the atmosphere canceling out most of the gravity. There is. For me it's the force of the chair on my butt. For the atmosphere, it's the air pressure.
So gravity doesn't "make the air rotate". The air is already going, and gravity simply changes its direction to pull it in a circle.
You may be wondering why the air doesn't just sit there and have the Earth spin underneath it. One answer to that is that from our point of view that would mean incredibly strong wind all the time. That wind would run into stuff and eventually get slowed down to zero (that's from our point of view - the air would "speed up" to our speed of rotation from a point of view out in space watching everything happen). Even the air high up would eventually rotate with the Earth because although it can't slam into mountains or buildings and get stopped from blowing, it can essentially "slam into" the air beneath it due to friction in the air. (This is a little redundant with dmckee's answer; I was half way done when he beat me to the punch)
Actually the path of the Foucault Pendulum is not "fixed" (even approximately!) to the "fixed" stars. Unless the pendulum is installed at one of the Earth's poles (as someone has done), then the point of suspension is in constant rotation with the Earth itself. $\therefore$ the pendulum is really not in an intertial frame.
Consider a pendulum at the equator, swinging in a North South plane.
It's obvious from symmetry that the plane of this pendulum doesn't
rotate with respect to the earth and that, relative to an inertial
frame, it rotates once every 24 hours. - UNSW, Austl.
A very good discussion of the forces (real and fictitious) on the pendulum can be found at this UNSW site. The vector that points from the suspension point toward the Earth is in constant acceleration and has a precession period that varies according to latitude.
This animation from the Wikipedia article on the Foucault pendulum may help show how the plane of the pendulum is rotating.
Best Answer
Yes, the "rotating Earth" model is preferred for the sake of simplicity. In fact, only in such "inertial systems", the laws of motion have the simple form in which the acceleration is determined by the force calculated via the inverse square law, and so on. All other inertial frames - moving by a uniform velocity and constant direction relatively to the first ones - offer the same simple laws.
The other frames, accelerating or rotating ones relatively to an inertial frame, don't admit a simple description like that. More precisely, their formulae for accelerations contain additional terms, the so-called fictitious forces – the centrifugal and Coriolis' force. These forces may be derived by transforming the simpler laws from the inertial systems to the non-inertial ones.
So the rotating frames – e.g. one in which the Earth is not spinning – are less good. Newton would recommend not to use them at all. Ernst Mach suggested that they are equally good and the fictitious forces result from some relative behavior with respect to distant stars. This view, Mach's principle, motivated Einstein to look for his new theory of gravity.
However, the final product, general relativity, didn't confirm Mach's principle in the original form. One may describe everything in terms of rotating frames – e.g. one in which the Earth is not spinning – but one must also include the corresponding modification of the gravitational fields which guarantee that the fictitious forces will be present.
As a result, one may still show that the spacetime is nearly flat around the Earth and this fact becomes manifest in the inertial (not spinning) frames, e.g. one in which the Earth is spinning by the usual rate. Ernst Mach would deny that the spacetime may carry any information about its being in a spinning state or not. However, according to general relativity, even empty spacetimes do carry this information about the geometry. And the geometry is only (nearly) flat in some (non-rotating) frames. The other frames may be used as well but the laws of motion in these frames will contain additional terms – the fictitious forces – which result from a "not explicitly flat" form of the metric i.e. spacetime geometry.