There was XML similar to this at the end of my project file:
<Target Name="EnsureNuGetPackageBuildImports" BeforeTargets="PrepareForBuild">
<PropertyGroup>
<ErrorText>This project references NuGet package(s) that are missing on this computer. Enable NuGet Package Restore to download them. For more information, see http://go.microsoft.com/fwlink/?LinkID=322105. The missing file is {0}.</ErrorText>
</PropertyGroup>
<Error Condition="!Exists('..\WebApp\packages\SPECIFICPACKAGE')" Text="$([System.String]::Format('$(ErrorText)', '..\WebApp\packages\SPECIFICPACKAGE'))" />
</Target>
By changing the ..\Webapp\packages to ..\packages like the rest of the file, my solution compiles just fine now.