I ran into the same issue with the Google API's. The main issue here is if you install the Microsoft Http Client Libraries it puts in your project an updated version of the System.Net.Http.Primitives DLL. The web.config assumes you are still using the default version of 1.5. There are two things that need to happen to fix it:
First: Update to the latest versions of Google API and Microsoft Http Client Libraries. You can install the updates via NuGet. Right click on your website, click "Manage NuGet Packages", select Updates on the left. At the time of this post some of the Google API's are prerelease only. You can install them via NuGet by selecting "include prerelease" on the top left of the update screen.
Second Update/add a dependentAssembly into your web.config. To do this you need to know the version of the System.Net.HTTP.Primitives.dll that was installed. Look in your bin directory within Windows Explorer. Find System.Net.HTTP.Primitives.dll, right click on it, select properties, and click the "Details" tab. Note the version located there. At the time of this post mine was 4.0.10.0.
Then add/update a dependentAssembly section for the correct version.
<runtime>
<assemblyBinding xmlns="urn:schemas-microsoft-com:asm.v1">
<dependentAssembly>
<assemblyIdentity name="System.Net.Http.Primitives" publicKeyToken="b03f5f7f11d50a3a" culture="neutral"/>
<bindingRedirect oldVersion="0.0.0.0-4.0.10.0" newVersion="4.0.10.0"/>
</dependentAssembly>
</assemblyBinding>
</runtime>
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