President Donald Trump on Tuesday night asked a joint session of Congress to set aside “trivial fights” and “work past differences of party” in order to act swiftly on his top policy priorities.

But Mr. Trump faces significant challenges in bringing lawmakers together. First, he needs to bridge differences within his own party on tax policy, health care and other matters. And he will also need support from Senate Democrats to pass much of his agenda, at a time when the party’s base voters are urging resistance.

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