The Coronavirus pandemic created a global crisis that prompted immediate large-scale action, including economic shutdowns and mobility restrictions. These actions have had devastating effects on the economy, but some positive effects on the environment. As the world recovers from the pandemic, we ask the following question: What is the public attitude towards climate action during COVID-19 recovery and beyond? We answer this question by analyzing discussions on the Twitter social media platform. We find that most discussions support climate action and point out lessons learned during pandemic response that can shape future climate policy, although skeptics continue to have a presence. Additionally, concerns arise in the context of climate action during the pandemic, such as mitigating the risk of COVID-19 transmission on public transit.