Taking on the Bryan brothers - the best doubles team in the world, and aiming to become the first pair in the Open era to hold all four major titles in a calendar year - on the main Arthur Ashe court here, which will be filled with partisan home fans, would put the frighteners up most.
The Scot and his English partner, though, are straining at the leash for an opportunity to reach the final four of the US Open.
Their solid 6-4, 6-4 win over Rohan Bopanna and Edouard Roger-Vasselin yesterday showed the growing understanding this relatively new pairing - seeded No.6 - has achieved.
Marray has already got one over the American twins, during his run to the Wimbledon title in 2012.
The defending champions, meanwhile, were down a set and a break against unseeded Canadians Daniel Nestor and Vasek Pospisil before rallying for a 6-7 (1-7), 7-5, 6-2 victory, yet will remain favourites.
"It perhaps suits us to be the underdogs," said Fleming."The atmosphere may be a bit like a Davis Cup-style atmosphere, the crowd will be right behind them. I have always said playing in a great atmosphere no matter if they are behind you or not is better than playing in no atmosphere at all. I can't wait to get out there.
"I have never hit or played on Ashe. I have only ever watched matches. They have been the best team for years but today they proved just why they are so good, a break and a set down but still coming back to win. They have that belief in each other and as a team. Hopefully we cab ruin their dream year. That obviously is our aim but all credit to them, they are an amazing team."
Marray, too, is eager for the chance to repeat his dramatic win over the Bryans at SW19 last year.
"To get the opportunity to play a pairing like the Bryans on Arthur Ashe in front of their own crowd is just brilliant," he said. "I have beaten them before so that can give me confidence. It was a big match at a grand slam but I came away with the win. Hopefully I can do it again."
Fleming and Marray are starting to show signs of forging a partnership in the absence of Ross Hutchins, who continues his recovery from cancer. This is their first slam together. And they are improving with every match.
"It was a great win for us," added Fleming, of their third-round victory. "The scoreline may have looked straightforward but it was a tough match - went a break down in the first and it was a slow start. We got a little bit fortunate in the second set but we felt like we were on top for pretty much the whole way through .
"We have been getting stronger with each match and have been improving. We played a lot better today than in the first round where it was a real battle to get through.
Serena Williams, meanwhile, beat fellow American Sloane Stephens 6-4, 6-1 to move in to the last eight.