Therefore, the answer to Joshua Tucker's question -- Is there a Republican mandate? -- is no.
If you really want to push it, one could say that a mandate is whatever a party or a politician can convince everyone that the voters are saying. Polling might be useful for that, but so might campaign rhetoric -- really, it's just whatever works.
But, no, if you're talking about some sort of specific instructions from the voters, as a whole, to politicians, as a whole, you're going to come up against the fact that voters don't know or care much about about specific issues of public policy. And even if that wasn't the case, the ballot is an incredibly poor tool for expressing much more than a preference for one candidate over another. Mandates are fictional.