There are many reasons governments want social media buy-in from management, and one strategy you can use to obtain it is to utilize the social traffic you'll gain from a major weather event.
Georgia's Johns Creek Police Department received a social media impact award for its efforts in communicating with the public on social media during a #Snowpacalypse event in 2014. The award was presented during the SUGA2015 event in Atlanta this April.
A significant weather event is likely going to happen in your area, whether it be a major snowstorm, wildfires, drought, etc. -- and odds are that you will get a lot of traffic to your social media profiles.
Use this traffic as an opportunity to gather data on engagement and reach of your social posts, and report this data back to management. Administrators love to make data-based decisions, and hopefully this means support for your social media program -- perhaps earning additional resources.