Story highlights Republicans will not find an exact ideological match in Donald Trump, says a GOP strategist

But it will be hard for the new president to break the inertia of Washington, he says

The Axe Files, featuring David Axelrod, is a podcast distributed by CNN and produced at the University of Chicago Institute of Politics. The author works for the podcast.

Alexandria, Virginia (CNN) Despite Donald Trump's strongly conservative cast of Cabinet nominees, a veteran strategist who worked for a pro-Trump super PAC predicts the new presidency will be unpredictable, at times confounding members of both parties.

"There's a lot of Democrat in Donald Trump. There's a lot of Republican in Donald Trump," Alex Castellanos told David Axelrod on "The Axe Files" podcast, produced by the University of Chicago Institute of Politics and CNN.

Castellanos, who initially opposed Trump's candidacy but supported him during the general election, believes the President-elect's lack of ideological rigidity "may help him become an effective president."

That's because while a chasm separates the Democratic Party from many of the policies Trump espoused on the campaign trail, Castellanos cautioned that instead of taking Trump too literally, one should view much of what he says like an opening bid in a negotiation.

"He's a dealmaker. He always starts somewhere beyond where he hopes to end up. So, yes, by definition, he's going too far," Castellanos argued, while referencing Trump's positions on free trade, his incendiary language toward immigrants, and his less than stout defense of America's commitment to NATO.

Read More