Installing Umbraco 6.1.5 directly via NuGet will cause some issues since some of the dependencies are downloaded in newer versions. Installing each dependency in the order as listed below will make sure that the dependencies are installed in the correct version.
Install-Package Newtonsoft.Json -Version 6.0.4
Install-Package Microsoft.Web.Infrastructure
Install-Package Microsoft.AspNet.Razor -Version 2.0.30506
Install-Package Microsoft.AspNet.WebPages -Version 2.0.30506
Install-Package Microsoft.AspNet.Mvc -Version 4.0.30506
Install-Package Microsoft.AspNet.Mvc.FixedDisplayModes -Version 1.0.1
Install-Package Microsoft.AspNet.WebApi.Client -Version 4.0.30506
Install-Package Microsoft.AspNet.WebApi.Core -Version 4.0.30506
Install-Package Microsoft.AspNet.WebApi.WebHost -Version 4.0.30506
Install-Package Microsoft.Net.Http -Version 2.0.20710
Install-Package MySql.Data -Version 6.6.5
Install-Package MiniProfiler -Version 2.1.0
Install-Package HtmlAgilityPack -Version 1.4.6
Install-Package Lucene.Net -Version 2.9.4.1
Install-Package SharpZipLib
Install-Package xmlrpcnet
Install-Package UmbracoCms.Core -Version 6.1.5