I ran into this same problem while working through the Contoso University asp.net MVC tutorial. It appears that the problem comes from mixing the SQL Server Compact connection strings with the Membership provider Sql Server connection.
I initially used hyperGeoMetric's fix, and that did work. Then I looked at the downloadable code's web.config and noticed some additional configuration.
If you add/replace the default parameter of entityFramework with this:
<parameters>
<parameter value="Data Source=(localdb)\v11.0; Integrated Security=True; MultipleActiveResultSets=True" />
</parameters>
add a system.data section like this:
<system.data>
<DbProviderFactories>
<remove invariant="System.Data.SqlServerCe.4.0" />
<add name="Microsoft SQL Server Compact Data Provider 4.0" invariant="System.Data.SqlServerCe.4.0" description=".NET Framework Data Provider for Microsoft SQL Server Compact" type="System.Data.SqlServerCe.SqlCeProviderFactory, System.Data.SqlServerCe, Version=4.0.0.0, Culture=neutral, PublicKeyToken=89845dcd8080cc91" />
</DbProviderFactories>
</system.data>
and modify the existing (default) DefaultConnection to look like this:
<add name="DefaultConnection" providerName="System.Data.SqlServerCe.4.0" connectionString="Data Source=|DataDirectory|aspnet-membership.sdf" />
After these modification, I was able to continue the tutorial using the Sql Server Compact edition.
Sam