Welcome to the wonderful world of large agency bureaucracy in the era of increasing caseloads and reduced staffing. You can check on the status of your application by following up with your Social Security office either by phone or in person. If you are getting no response from the messages you presumably leave at your local office, it may be quicker to go down there one day, take a number and wait to speak to a live person. Since I am certain you are not working as you do not have a social security card, you could spend the time at their local office - it might not be that long of a wait if you go early in the day.
You could also try calling the general social security 1-800-772-1213 number, but since that automated system asks you for the social security number you are calling about right up front you would need to hit "0" (the number zero not the letter 'o') repeatedly to get to an agent - then you could ask that person for a supervisor's name and telephone number at your local office since you never get a response to the messages you leave for your local office - they should give you that information but generally are reluctant to do so so you may have to nicely push them to give you the info - remember you catch more flies with honey than with vinegar.
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The only other isea is to contact your local US Representatives' or your local US Senators' offices and ask for help. They usually have someone on staff who deals with just these sort of problems and are able to get things done. Their telephone numbers are usally in the phone book under Government Offices.
Good luck to you.
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SSA's website says they mail the social security cards upon receipt of all information. It's only been a couple of weeks since you applied, and the holidays always cause some delay in getting mail because the Post Office has tons of extra mail to handle.
Another factor may be that Las Vegas has a special social security card center which processes applications for SSNs. That center may have a backlog. Keep in mind that, at the end of the calendar year, a lot of employees take some vacation time and that causes some delay in processing, as well.
You could always tell your Senators and Congressperson that SSA needs more funding, so that more employees can be hired for tasks such as SSN processing. SSA funding has significantly decreased over a number of years, with a few increases lately, but the latest budget is not enough to keep up with rising costs and there has been some talk of furloughs. If that happens, SSN processing and other tasks considered lower priority will take even longer.
This communication does not establish an attorney-client relationship. This communication offers general information based on the limited facts set out in the question, and does not constitute the giving of legal advice. For specific legal advice, consult an attorney in your state who is knowledgeable in this area of law.