Borrowing money to cover debt service assures bondholders?

For these reasons,  the Department of Treasury has always emphasized – regardless of which party has held the White House or either house of Congress – that the only way to prevent default and protect America’s creditworthiness is to enact a timely increase in the debt limit. Says Deputy Government Treasury Person

HT Karl Smith
Now, I would think that borrowing money to cover debt service would scare the shit out of bondholders. Existing bondholders would be much more assured if you didn't borrow any more money and still stayed within budget.