Obviously the GOP-controlled Senate was not going to approve the Green New Deal proposal, and Alexandria Ocasio-Cortez, Sen. Ed Markey and other supporters of the idea recognized that the Democratic Party was and is badly split over this idea. The main reason that Mitch McConnell, the crafty old Senate Majority Leader for the GOP, brought the GND to a vote was in hopes of splitting the Democrats and getting them to fight each other rather than the Republicans.
Most of the Democrats, including Ed Markey and other supporters of the Green New Deal, therefore took the smartest option and decided not to vote either for or against S. Res. 59, the Green New Deal's legislative number in the Senate.
This way the Democrats in the Senate kept their sense of unity and put off intra-party debates and discussions over the Green New Deal until a later day. They recognized that it would have been stupid for them to walk into the political trap Mitch McConnell was setting for them.
A few Democrats, mostly ones from coal-producing states (like Sen. Joe Manchin of West Virginia) voted with the Republicans against the proposal, because they don't mind wrecking the damned planet and condemining the people of the United States to future damage from hurricanes, floods, western wildfires and other manifestations of climate change -- not so long as coal company profits can be preserved.
Most Democrats in the Senate, though, wisely decided to take their time in deciding whether to back the Green New Deal on some future occasion.
-- democratic socialist for a Green New Deal -- even though it's kind of interesting to see climate-related disasters sweeping across "Red" states in the Midwest, in the form of terrible floods, while Republican voters in Florida, Texas, and North & South Carolina struggle with homelessness & business losses from recent hurricanes