It's not normal... nor is it how the US government works, not even in this dispute.
Bill paying is up to the Treasury in the Executive Branch, which has enough revenue to pay its bills. The Treasury takes in money on a daily basis throughout the year, and the amount it takes to service the debt, again on a daily basis, is much less than what it takes in.
Regardless of the #DebtCeiling the Treasury, according to its own reports, has the money it will need to pay its bills as they come due.
The real solution to this is for Congress to stop authorizing spending of money without providing financing for that spending.
The US can and the president legally MUST pay their bills.
The debt ceiling isn't the cause of this dispute. Bad governance and misleading political rhetoric is.