Probably not. There is a limit on the amount of time they would have to respond to a lawsuit, but, from your question, it does not sound like you have filed a lawsuit.
However, it is likely that Wal-Mart has an arbitration agreement that covers claims for damages to your vehicle (it would be found in the fine print in the paperwork you received when you took the vehicle in). If this is the case, the arbitration agreement, rather than typical rules of lawsuits and court, will cover your situation.
Without seeing the agreement, I can't be sure, but I would bet that any claim for damages is supposed to be in writing, so the time limit for a response(assuming there is one in the arbitration agreement) won't begin running until you submit your claim in writing.
At this point, however, it is likely in your best interest to speak with the manager to try to resolve this matter. Given the amount of damage involved, it is unlikely an attorney would take the case on a contingency basis, and if you pay hourly, you would pay way more in attorney's fees than you would ever recover from Wal-Mart.
Outside of the PR benefits, they have no reason to respond. If they do, it will be a generic response that is meaningless.
If you can't work it out with the shop/bay manager, you will likely have to file a small claims complaint.
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Give them a call and ask them what they intend to do? If they are stalling prepare, file and have them served with a small claims complaint. You will need two credible estimates of repair and that will be your damage along with cost of 5 quarts of new oil if that will be an additional cost as well? You should also claim any mileage you will incur to get the estimates and return the car to another shop for repair, as well as any towing fees? In California we have the Bureau of Automotive Repair which is under the Department of Consumer Affairs. As Walmart is a Corporate Giant that may not respond to you, maybe you should see if you have a similar agency and can file a consumer complaint with them if Walmart doesn't stand by their work and offer to repair your car. Good Luck!
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In addition to the other answers, some states have agencies that license and regulate car repair facilities. They may have rules regarding repairers responses to complaints. Look at your state's website, You can also check with a local consumer law atty for help/advice.