Prior to their second-round match in Melbourne, his opponent Sam Groth quipped: "Be nice if his wife went into labor overnight. I might just be cheering for that one."
There was no such luck for the big-serving Australian, although the way Murray played Thursday it seemed like the twice grand slam winner had a plane to catch.
The Scot, ranked second in the world, beat Groth 6-0 6-4 6-1 in one hour and 31 minutes to move into the third round at the year's first major.
There will be tougher tests for Murray, assuming he doesn't have to rush back home -- the baby is due the second week of February -- but he put in a stunning performance against the player who took a set off Roger Federer at Wimbledon a year ago.
Murray repelled Groth's huge deliveries, picked off the world No. 67 at the net and authored winning lobs with his foe stranded.
For tennis fans, it may have been the perfect antidote to allegations of match fixing
and not trying, or tanking, in matches that took place on the tour years ago. In the latter instance, Murray's pal, Novak Djokovic, on Wednesday refuted claims
he deliberately lost a match at the Paris Masters in 2007.
It's an important year for Murray, parenthood no doubt leading the way.
On the court, Murray is seeking a first grand slam title in three years. Despite finishing at No. 2 in 2015 and leading Great Britain to a first Davis Cup title since 1936, one could argue that the second best player in the world last year was Federer. He and Djokovic contested the Wimbledon and U.S Open finals, with Murray's lone appearance in a grand slam final in 2015 coming in Melbourne.
Having to face Djokovic in another final this fortnight would be problematic for Murray, since he has lost 10 of their last 11 meetings.
Yet Murray's path to the semifinals is gentle and if someone does happen to beat the red hot Djokovic prior to the finale, his chances of achieving a third major would significantly increase.
Murray's next challenger is 32nd seed Joao Sousa, a scrapper from Portugal. Murray leads their rivalry 6-0, surrendering just one set.
Azarenka continues to cruise
In women's action, Victoria Azarenka matched Murray's sizzling performance. Azarenka, like Murray a two-time grand slam winner, pummeled Danka Kovinic 6-1 6-2, a round after thrashing Alison van Uytvanck 6-0 6-0.
Azarenka has been hampered by injuries lately, most notably in 2014, but appears to be ready to add to her grand slam collection. She's also an artist.
The former No. 1 triumphed at a tournament in Brisbane in early January and hasn't dropped a set through seven matches in 2016. On average, she's conceded less than three games per set.
Azarenka has thus had plenty of reason to perform her "dab" celebration, popularized by NFL quarterback Cam Newton.
He "made it viral and we happen to have the same agent, so I wanted to make my agent smile first," said Azarenka, who next plays promising Japanese slugger Naomi Osaka. "Then Cam heard that I started doing it. I know. I just love the sign. I think it's cool."
Garbine Muguruza defeated Kirsten Flipkens 6-4 6-2 and the third seed was joined in the third round by former No. 1 Ana Ivanovic, who overcame Anastasia Sevastova 6-3 6-3.
Back to the men's draw and later Thursday, home favorite Lleyton Hewitt takes on eighth seed David Ferrer in a match much of Australia will be tuning in to.
Hewitt, playing in his 20th straight Australian Open, is retiring after the event.
Tributes have poured in over the past few months and Murray offered up one of his own.
"I actually named my dog after him," Murray said in an on-court interview, drawing laughter.