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Having debt in the US does not automatically prevent you from getting a US visa. Nor will you be arrested at the airport just because you have debt.
On the other hand, one of the things you need to do to get the visa is to show that you can support yourself for your time in the US (without of course working). That becomes much harder to demonstrate if you have substantial debt, regardless of what country that debt is in.
Likewise you have to show that the money you spend on your US visit is reasonable for you to spend given your financial circumstances. You don't state the reason for your wanting to visit the US, or where you are visiting from. but (for example) people with thousands of dollars of debt who are trying to pay it back don't take expensive overseas vacations. On the other hand if the visit was business related and your employer was paying the costs that would be different.
So the short answer is that the debt is not an automatic barrier, but can be a negative factor in your visa application. How much of a negative factor we cannot determine.