He's cheated on his core supporters, without any explanation, too many times.

Each party consolidated its core supporters and won half the independents.

Both campaigns have made an extra effort to steal each other's core supporters.

"We've got to keep our core supporters and also attract the new."

This would turn off his own core supporters to a huge degree.

"He's struggling because a lot of his old core supporters are dying off."

A top campaign staff member, called the "base vote director," is largely concerned with turning out core Democratic supporters, including black voters.

In part, the charges are designed by each party to get out their core supporters to the polls.

What sort of political position does that put you in with your core supporters?

He has made an effort to reach black voters, who are some of the Democratic Party's core supporters.