Visiting USA with a transit visa

If you have a C visa, you can't use that.

Transit (C) visas are nonimmigrant visas for persons traveling in immediate and continuous transit through the United States en route to another country, with few exceptions. Immediate and continuous transit is defined as a reasonably expeditious departure of the traveler in the normal course of travel as the elements permit and assumes a prearranged itinerary without any unreasonable layover privileges. If the traveler seeks layover privileges for purposes other than for transit through the United States, such as to visit friends or engage in sightseeing, the traveler will have to qualify for the type of visa required for that purpose.

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Travel purposes not permitted on a Transit (C) visa - Examples

• A foreign citizen whose layover in the United States is for a primary purpose other than to transit, for example to visit friends or sightsee, requires a visitor (B) visa.  _{– State Department}

In other words, you can only use a C visa if your purpose for entering the USA is just to be there briefly catch a flight (or other means of transport) to another country. That might take a few days (e.g., if flights are infrequent or if you were taking a train from Canada to Mexico) but I doubt your 12-day visit is just to catch a plane.

When you arrive on a transit visa you will have to pass immigration. If you are trying to stay for 12 days they will most likely send you back home as that is not transiting, that is tourism. If you "Miss your transit flight", stay for 12 days, then go back home, you will prob be denied future entry into the US and have problems for at least the next 10 years visiting or transiting the US.