Company XYZ plans to invest $20 million this year on a new factory, conditional on getting a loan with an interest rate of 10%. However, the government decides to introduce stimulative fiscal policy by building new highways. In order to conduct this operation, the government needs to borrow money,
and since they are such a big player (in the US economy) their decisions will affect the market for loanable funds (money available for loans). In order to make sure there is an adequate supply of loanable funds for everyone demanding them, the banks must raise their interest rates. This does two things: it reduces the quantity demanded of loanable funds because it had become 'more expensive' to borrow, and it increases the quantity supplied of loanable funds, because people are getting a higher return on their savings.
So lets go back to our company XYZ example, because they were planning on spending $20 million when the interest rate was 10%, maybe now the interest rate is 15% because of the increase in government spending. This increase in the rate makes borrowing more expensive so they are likely to invest less now, maybe only $15 million. This decrease in $5 million is a result of the crowding out effect. Because of government actions, this company has decided to invest $5 million less than it normally would have.
So how does this current debt deal relate to the crowding out effect? It should shift the demand for loanable funds left, reducing both the interest rate and the quantity of loanable funds. This should cause an increase in private investment. However, remember that the change in private investment isn't a direct result of government expenditure, it is a response to the change in the interest rate. So we will have to wait and see if their is an associative change in the interest rate, then maybe we will see private investment fill in the gap created by the decrease in government spending.