Do labor taxes give illegals an advantage in service business?

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Not all states have labor taxes, but in Texas we do, some people have chosen to close their service related business like lawn care and house cleaning due to this. It seems to be an unfair advantage to the illegal aliens as we citizens have to pay taxes on income, tips and collect and pay taxes on services.
Some customers complain about the labor tax and that not everyone collects this tax and they think they are being ripped off when you follow the letter of the law.

I will contact my congressman to complain, as it seems like taxation without representation, but what could I say to best prove my point? What info and how can I get it to support my argument?