Control arms

It depends on what is wrong with it. If the rubber bushings are worn, it will prevent the arm from holding that wheel in proper alignment. In a week you are likely to not observe bad tire wear patterns, but this doesn't happen in short order. Worn bushings get progressively worse over time, so this has been going on for a while.

Along with the accelerated tire wear, correct alignment contributes to stopping in a straight line, and it can adversely affect steering control and response.

If the arm is bent, that also affects the alignment, but with worn bushings, the alignment moves around with changing road forces. A bent arm holds the wheel solidly in position even though it is the wrong position.

If you're referring to the front lower control arms, those come with the ball joints riveted to them. Those joints can be replaced separately without having to replace the entire arm. If the joint is the reason for replacing the arm, I'd be real nervous about driving the car. One car brand in particular is famous for those ball joints separating, leading to loss of control and crashes, so squeaks and rattles must never be ignored. With GM products you have a little more warning, and you will likely get by for a week, but again, it depends on the reason you need to replace these arms.

Your car also uses a number of rear control arms. Those affect the alignment of the rear wheels, so they affect handling and steering control as well as tire wear patterns. Due to the design of their bushings, there is nothing that can separate leading to a total failure as can happen with a ball joint. That assumes they aren't about to fail due to rust. Rusty control arms can break without warning, sending you into the ditch or into oncoming traffic.

What is wrong with the control arm? Which one is it?

That still leaves things unanswered. Having the car towed insures you won't get swallowed up by a safety problem, but it could be an unnecessary expense depending on what is wrong. "Lower" control arms suggests it's the front ones you're referring to. If the bushings are worn, it can be hard to know which way the car is going to go when you hit a small bump in the road, but they won't suddenly fall apart. If the ball joints are worn and sloppy, that happens over a fairly long period of time and gets progressively worse. You'll hear occasional clunking too. I'd drive the car to the shop if that distance isn't too far. It might be too big of a chance risking driving it for long distances.