Despite National winning the party vote in Roskill in 2014, Key spent much of a media standup talking down the chances of Parmar, who was standing at his shoulder.
"The expectations would be that we would lose. We are the underdog and because no incumbent government has won a seat that they don't hold [in a byelection]."
Parmar was the best candidate, Key said, but there was "relatively little" at stake for National.
"I think if Roskill was to go National, then I think it would really be terminal for Andrew Little. If they lose Mt Roskill I just can't see how he would be able to return to Parliament and argue that he could be the leader of the Labour Party," Key said.
"There would be no expectations for us to win. This seat has been held by Labour forever, and the reality is what we have done over the years is got a few people who have supported Phil Goff to give their party vote to National."
Little will campaign in Mt Roskill tomorrow, and attend Labour candidate Michael Wood's election night function.
Key won't be at Parmar's - he said he doesn't attend byelection night functions and that wasn't a reflection on his MP's chances or campaign. Key has attended byelection functions in the past, including when Jami-Lee Ross won Botany in 2011.
Earlier, Parmar was largely a spectator as shoppers and staff lined up for photos, although the Prime Minister's security detail ushered away one man who leaned in to tell Key he was a wanker during a walkabout at Royal Oak Pak'n Save.
Staff gave Key packets of Christmas mince pies as he left.
At Stoddard Rd Countdown a manager gave Key a rundown about the pricing of $1 cans of Oak spaghetti.
After spotting a bottle of Moscato Rose in a shopper's trolley, Key told her how popular the wine had been at his son Max's 21st birthday.
"They drank everything we had in about an hour. Unbelievable. Buy more than what you think you need, that is my advice."
Roskill voters will on Saturday decide who will replace Goff, who quit Parliament to become Auckland Mayor.
Apart from a three-year break between 1990 and 1993, Goff has been the Mt Roskill MP since 1981, and had an 8000 majority in 2014.
However, an upset in Roskill is possible particularly if there is a low turnout. Boundary changes have added areas with more National-leaning voters.
In 2014, National got 14, 275 party votes - 2000 more than Labour - but one quarter of
National voters opted for Goff.
Key backs MP-in-waiting
If Parmar does win Roskill, National will gain a seat and the next candidate on its list is Misa Fia Turner, who stood in Mangere in 2014.
Turner was born and raised in Samoa, has lived in Mangere for more than 20 years, and is the co-founder and clinical manager of 'Malu I Uo Faatuatua Family Relationship Services, which provides counselling, mediation and mentoring.
Her social media shows she is a Donald Trump fan who also believes in stigmata -
body marks, sores or pain in locations corresponding to the crucifixion wounds of Jesus Christ.
Asked about those views today, Key said he hadn't seen the posts and so would not comment. He blamed Labour for the scrutiny of Turner's beliefs.
"We certainly back her. What it shows you is how worried Labour are about the byelection - because the reality is that they are now getting to the point where they are so concerned they might lose, that they are now focussing on the fact that if Parmjeet was to win the seat, Fia Turner would come in."
Turner has previously been in the news after Labour questioned her right to use the "Misa" Samoan chief title.
