They will litigate Cruz eligibilty to be president, they've said so. Don't expect it to go anywhere, but the constitution hasn't been tested regarding this yet.
In the General Election they will hit Cruz hard on his flat tax position. I don't have a problem with a flat tax but the Dems will end up making him look like a kook.
Cruz is calling for the elimination of the Department of Education, Energy, Commerce, Urban Development to name a few. They'll use this to make Cruz out to be the Grinch who stole Christmas.
As much as most of us like Cruz, he'll need to appeal to lot more folks to be President.
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There is no basis for litigation.
It would take less than a day to establish that fact, even if they found a mentally retarded Carter judge to make a ruling, it would be overturned before the sun set.