Matt Harvey is scheduled to pitch on Friday, but next in line for Saturday would be Gee who would be pitching on three days rest.
I don't see the Mets sending Gee out in that game. I would expect the Mets to call somebody up from Las Vegas to make that start instead.
The most obvious candidate for that start is Collin McHugh. He is on the 40-man roster, and is probably their best option not named Zack Wheeler. However, McHugh is starting later tonight against the Sacramento River Cats in Las Vegas; if McHugh pitches tonight, that would rule him out for Saturday's start against the Nationals as well.
It's worth noting Saturday is April 20, which is exactly 20 days since the start of the season. Per MLB rules, a player accrues a full year of Major League service time if he spends 172 of the 182 days on the active roster or on the Major League disabled list. If a player is optioned to the minor leagues for 20 days or less, he is credited with big league service time as well. And so, even if the team would consider Wheeler for Saturday's start, his service time would be retroactive to the start of the season because of this rule, meaning he would accrue enough service time to not only become 'Super Two' arbitration eligible after next season, but eligible for free agency after the 2018 season.
As I've said before, I don't believe the organization is so much concerned with Wheeler becoming 'Super Two' eligible as they are accelerating his free agency clock. But regardless of that, Wheeler has gotten off to an uneven start to his season with his command, and so I think he needs to show more consistency before being considered for a big league promotion.
Then again, if tomorrow's game is snowed out in Denver and they decide not to play a doubleheader on Thursday, they could bump Hefner to Saturday, which would keep them from scrambling for an arm altogether...