He and his wife, Rebecca, are also dreaming of the birth of their baby girl.
The two dreams are about to become reality at the same time. Bresnik will be on a mission in space when Rebecca is scheduled to give birth.
"I will admit the first day we found out there would be a conflict, I was like, 'Why can't you change your mission?'" Rebecca Bresnik, 40, told "Good Morning America."
But Randy Bresnik, 42, has been in training for years. With just a few flights remaining in the space shuttle program, this would be his only opportunity.
Bresnick is a lieutenant colonel in the Marine Corps and served in Kuwait supporting Operation Iraqi Freedom. He will be a mission specialist on the Space Shuttle Atlantis, which is scheduled to lift off this afternoon from the Kennedy Space Center in Cape Canaveral, Fla.
The crew's 11-day mission is to deliver spare parts and supplies to the International Space Station. Astronauts are expected to make three space walks.
Rebecca Bresnik, an international affairs lawyer for NASA, is scheduled to give birth Thursday. The birth is being induced for medical reasons.
The Houston couple have run into scheduling conflicts before.
Randy Bresnik missed his first day as an astronaut because he and Rebecca were getting married in Scotland. He said if he had to miss his daughter's birth, the mission is "a pretty good reason."
"I can't believe how blessed I am," he said of the upcoming birth and his chance to go into space.
They were amazed when Rebecca got pregnant, because they'd been told the odds were one in a million she would conceive.
Their 3½-year-old son, Wyatt, whom they adopted last year from Ukraine, had been home for three months when they found out she was carrying a child.
"I still look down every day and say 'Oh, my gosh, I'm pregnant. Oh my gosh, I'm pregnant,'" she said, speaking of her husband, "He does the same thing.
"After being told for five years that we'd never have a biological child ... I can't squabble about a delivery date," she said.
Asked how he would feel about being in space when he found out about the birth of his daughter, Bresnik replied: "To imagine that miracle coming from inside her ... even though the space station is big ... I don't think it will be able to contain my smile."
Bresnik wouldn't be the first dad in space to miss his baby's delivery.
Astronaut Mike Fincke coached his wife, Renita, through labor in June 2004 while he was on the International Space Station. He talked with her by radio while the space station orbited 225 miles above Earth, and welcomed a baby daughter, Tarali Paulina.
The Bresniks have not yet picked out a name for their daughter.
ABC News' Kelly Hagan contributed to this story.