Is this worth canceling the purchase?

My hubby and I bought a used 2012 Honda Civic LX 31K miles from a dealership last night. While we were test driving, we heard a light rattling noise but other than that the car drove great and we were allowed to take it far enough to test the brakes, acceleration etc.

The car was sold to us at a reasonable price - price that could have been lower but fit the price range on Kelley blue book and NADA.

Anyhow we explained the rattling noise to the dealership and they said they'd check it out today and so we left the car at the dealership overnight. Today the service advisor from the dealership called us and said it's the shift cable rattling and that they'd have to get the parts to get it fixed. Given that it's Labor weekend, it would take Tuesday to have it fixed and ready for us. We're not paying for this repair but we're taking this is as a red flag since we JUST purchased this car and it already has a problem. What would be the right course of action to take if anything?

We didn't drive off. We parked the car off at the dealership overnight.

Did the dealership give you any timeframe that they allow cancellations? Once ink is on paper, and you drive off, you're an owner. There's no right of rescission in vehicle sales (one exception: CA, where you have a 48-hour period you can purchase at point-of-sale).

A Civic is a reliable car, and it has low miles. A loose cable is not a big deal, and I don't think you can use that to make any other comment on the car's quality. And if you need a another car, how do you know it is any better than that car?
CA does have a cooling off period, but the car buyer has to pay for that option, like $400, or can decline it.
If you are not in CA or are but did not buy the option then you own the car, there's no right to return it.
I think you are fine, sounds like buyers remorse, which is normal. I think the best course of action is to use that rattle to ask them to take a look at it and find if there are any other issues, it is just bit of leverage, you are saying Hey, you missed something simple, so lets just double check everything.
Not that you have any right $1 of repair, but the dealer most likely wants to make sure you are a happy customer and might come back for your next car.

First check as to whether the purchase can be cancelled or not----depends on your state laws and the contract. Secondly, the honda civic has a very good reliability record---I assume you did carfax on the car to get repair record and with 31K miles some warranty must be left on it.

You don't have the right to cancel the deal. The dealer may CHOOSE to accept the car back, but they are under no obligation to do so and you could forfeit any money you have paid. The car is still under the factory warranty, just have it repaired.

You usually don't have the option of cancelling.

If you left a deposit and didn't take the car, you can cancel but you probably lose the deposit.

In some states, if you haven't taken delivery of a vehicle (taken it off the dealer's lot), the deal hasn't been completed, and you could back out. However… I see no reason to panic over such a small problem that the dealer has agreed to fix.