Remarkably, their birth heralded the arrival of the second set of sextuplets in the United States within a day after a 24-year-old woman delivered six of the best late on Sunday in Minnesota after using fertility drugs.
This rare occurrence could become more common as more couples seek artificial methods of conception.
They will be named Bailey Elizabeth, Savannah Jane, Molli Grace, Cole Robert, Blake Nickolas and Grant William. The Masches have yet to decide who gets which.
The heart problems were due to the huge volume of blood that Jenny Masche was carrying in her body while pregnant, Doctor John Elliott said at a news conference at Banner Good Samaritan Medical Center in Arizona.
The new mother is now stable and is expected to leave the hospital's intensive care unit later today.
Exhausted and wiping tears from his eyes, proud father Bryan Masche said: "I'm very thankful that we had the help of the best physicians, and the best doctors and the best medicine."