Well, obviously, we want all would sleep better at night with a balanced budget.
Would we?
The $1Trillion would not be borrowed through the issuance of government securities like Treasury Bills. Those who would have otherwise bought the securities would look somewhere else to buy some similar investment paper, perhaps buying previously issued US securities from some other investor or perhaps buying some other securities -- state bonds, other countries bonds, something else, who knows.
At the same the the $1Trillion would not be spent but the US there by reducing GDP by more than $1 trillion, due to indirect effects of laying off government workers, reducing orders to vendors and reducing the demand for government contractor work.
So yes, drag on economy.
The effect on people's work and spending habits depends on who, what and how is taxed. How this may or may not drag on the economy is hard to tell without more specifics about the tax plan.