No, not blackmail.
The president is requesting additional power to borrow money, and as per checks and balances, he only gets that power if our representatives agree that it's for the best for the country.
It has nothing to do with fault. It's just how the US was designed to work: if generations of Americans are going to be on the hook for paying off that debt, we want to make sure the public is really in agreement with it, through our democratic process.
If the president can't make his case for more borrowing to the elected Congress, then checks and balances means he can't borrow on our dime.