"How would a debt default by the federal government impact the home mortgage market?"
We can only guess about the extent of the impact, but it would range somewhere between ugly and catastrophic. Ugly might be a doubling of interest rates and a drop of 50 percent in loan volume. Catastrophic would mean an almost complete shutdown.
About 95 of every 100 home loans being written today are placed into mortgage-backed securities that are sold in the market with guarantees by Fannie Mae, Freddie Mac or Ginnie Mae. These are federal government guarantees, the value of which would drop like a rock with a default.
At best, the securities market would immediately demand a sizable rate premium on new guaranteed mortgage-backed securities to compensate for the added risk. This would immediately translate into sharply higher interest rates charged to new borrowers.