I searched the phrase "neutral is an invalid culture identifier" and found that it can be linked to either an empty string used as the culture, or using the generic culture, such as "en" rather than "en-US". As this is not an easily reproducible issue with NuGet in general, I would focus on any customizations you or your org have done with your NuGet, and even your Visual Studio and PowerShell, implementations.
As the Package Manager Console is running PowerShell and accessing instances of Visual Studio classes, I'd focus on add-ins to both PowerShell and Visual Studio on your machine. Also, NuGet packages you've installed can add functionality to the Package Manager Console, so it could even be a poorly written PowerShell function from a NuGet package you've installed. Any package that had an install step to run a Console command to configure the installation is suspect. (For more information, see "Extending The Package Manager Console With Packages" on http://docs.nuget.org/docs/start-here/Using-the-Package-Manager-Console.
Also, if you start Visual Studio with no solution, do you still get the error? That would help you figure out if it's a NuGet package adding PowerShell functionality or if it's something more base in your system's PowerShell or Visual Studio configuration/implementation.
As the Package Manager Console is running PowerShell and accessing instances of Visual Studio classes, I'd focus on add-ins to both PowerShell and Visual Studio on your machine. Also, NuGet packages you've installed can add functionality to the Package Manager Console, so it could even be a poorly written PowerShell function from a NuGet package you've installed. Any package that had an install step to run a Console command to configure the installation is suspect. (For more information, see "Extending The Package Manager Console With Packages" on http://docs.nuget.org/docs/start-here/Using-the-Package-Manager-Console.
Also, if you start Visual Studio with no solution, do you still get the error? That would help you figure out if it's a NuGet package adding PowerShell functionality or if it's something more base in your system's PowerShell or Visual Studio configuration/implementation.