tell us more about the coupons on bonds and accepted yields at auction
Your wish is my command.
At auctions for government bonds, investors decide how high to bid by considering two properties: The bonds' time to maturity and their coupon. Investors then compare this to their own time preference: What does the annual yield of their loans have to be so that $100 in the future, plus compound interest, plus appreciation, minus the statistically-expected loss from default, equals $100 now? Hence, from the expected future benefit, investors calculate backwards to get the maximum price the government's promise is presently worth to them.
With that in mind, I can amend my earlier answer as follows: Unless the government has lost all
its credibility with lenders, it can always
sell all of the bonds it offers. The question is at what price. But that doesn't change the substance of my earlier answer: Both reactions, accepting a lower sales price and offering a higher coupon, have the effect of increasing the bond's total yield.