Neither Hanson nor Sheets has never appeared in the Majors as a reliever.
The Braves planned to give Cristhian Martinez the day off Tuesday after he had pitched for three straight days.
Gonzalez brought Martinez into Monday night's long game. The right-hander came on in the 12th inning, threw 1 1/3 innings and took a hard-luck loss.
He gave up three infield singles in the 13th, and the Nationals got a win despite not hitting the ball out of the infield.
"We'll lay off of Cristhian for sure, today," Gonzalez said prior to the middle game of the series.
Gonzalez said if Martinez had gotten through the 13th Monday, then closer Craig Kimbrel would have come on in the 14th.