Roscommon scraped past the side from the Big Apple earlier this month.
Connacht Council secretary John Prenty has admitted that were New York to take a scalp in the province, it would create huge problems.
After a recent match in which they pushed Roscommon to the brink, the prospect of New York claiming a win is becoming a very real possibility for the council in Connacht, and it is an outcome they have admitted they are not fully prepared for.
Speaking to The Irish Independent, Prenty said "you'd have to take it at face value that if New York won, they'd be playing Leitrim in Carrick on Sunday week, that's what we'd be hoping.
"I assume we'd have some kind of row going on at the minute if it did happen. But we'll have to wait until some day it does happen and it will probably cause a problem. I wouldn't like to say you'd hope New York wouldn't win but it would be a major financial burden on Connacht if they did win."
While he highlighted that London have won in the past, Prenty noted that having the side from the United States involved would be a headache both logistically and financially.
Speaking to Newstalk Sport this week, Cathal Cregg of Roscommon noted that New York have a number of players who have been at the inter-county level before, and believes it's only a matter of time before they claim a scalp.
"We're not the first to have a scare over there," said Cregg. "Galway has a scare a couple of years ago. Someone will get caught over there, there's no doubt about it. Thankfully it wasn't us."