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why does the US operate at a deficit?are you talking about a trade deficit (the US operated at a trade deficit virtually the entire time it grew from 13 former colonies to the post WWII economic colossus. Lending money to a growing economy so it can turn around and purchase the equipment you are selling which it will use to be more productive is the secret sauce of a growing economy)
or are you talking about a budget deficit? many countries around the world operate with budget deficits; "socialist" governments generally have higher deficits as they spend to maintain living standards whether the economy justifies it or not. The size of the deficit (they will grow all the time) does not matter, what matters is "as a %age of GDP".
none of this, btw, has much to do with monetary policy, the maintenance of the currency.
"strong" or "weak" currency really makes no difference. The strength/weakness of the currency how the books are balanced after the fact of what has happened in the actual economy. A country with a strong currency will find imports inexpensive, and will have trouble selling its goods, and citizens will be incented to buy imports. A country with a weak currency will have difficulty importing goods, but will have less trouble exporting. It's the currency that balances these books.