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Connie Morella, who served eight terms as a Republican congresswoman from Montgomery County before losing in a gerrymandered district in 2002, said many of the state and national parties’ views on social issues and immigration have alienated women and minorities to the point that they are hurting the party.

“It’s time for [Republicans] to realize that our state is becoming more minority than majority,” said Ms. Morella, a longtime moderate who is now a professor at American University. “They have got to show that they are part of the community and care.”

Larry Hogan, a former GOP political candidate who now chairs the group Change Maryland, which has railed against Democratic-driven tax increases in the state, said Republicans can unite both their base and non-Republicans by focusing on one issue: the economy.

He said Marylanders on all points of the political spectrum have grown concerned with tax hikes and annual budget growth in the state. The number of independent and third-party voters in the state has grown in recent years, he said, as a result of Democrats leaving the party because they think it is becoming “too liberal.”

“Most people want private-sector growth and jobs, not government,” he said. “If we can find places to agree with some folks who don’t agree with us on every issue, then you can start to make a difference.”