The NBC comedy - starring Will Arnett and Christina Applegate - has pulled in a season average of 4.51m viewers, with 1.88m in the key 18-49 demographic.
"My thing is always that I try not to be too positive, because I feel like that's a jinx," Spivey told TVLine. "I'll assume the worst and then everything is a pleasant surprise."
The showrunner added that NBC has been "super-supportive" of the sitcom, which also features Jennifer Hall and Maya Rudolph.
"[The network has been] lovely to work with," insisted Spivey. "They seem to like the show, so fingers crossed."
The latest episode of Up All Night attracted a season low of 2.58m viewers.
The show's first season concludes tonight at 9.30/8.30c on NBC.
Watch a clip from Up All Night below: