The museum group has said it needs $23 million from the private sector, $15 million from the federal government and $8 million from the state to build.
The request for state money was spread out over three years.
"It's not that anybody's not doing their job or we're not being supportive," said Del. Sue Hecht, D-Frederick/Washington.
A key element is whether the Smithsonian Institution would be affiliated with the museum.
In his letter, Frye promised Glendening that the Smithsonian would commit to the museum if there were state funding.
Representatives of the Smithsonian's affiliations division could not be reached for comment Wednesday.
"This museum is not a museum," Frye said. "It's economic development. It's jobs. It's tourists in our motels. It's tourists in our restaurants. ... It's cash registers and millions in hard cash."
Frye referred to Pennsylvania as a model, in light of the proposal Gov. Tom Ridge announced Monday of $100 million for "historic infrastructure."
Of that, $80 million would go toward refurbishing the State Museum in Harrisburg, which includes a Civil War wing.
Ridge spokesman Steve Aaron said the wing features a 32-foot-by-16-foot canvas depicting "Pickett's Charge," a Confederate attack at Gettysburg. The state legislature commissioned Peter Frederick Rothermel to paint it and other pieces a year after the war ended.
An interpretive sound and light system explaining the painting will be one of many improvements, Aaron said.
A $36.9 million Civil War museum is already in the works in Harrisburg. Ridge gave out $16.2 million in state funding for the museum in July.
The Washington County Civil War museum would work well with Pennsylvania's, helping to build a tourism region, Aaron said.
Frye said the Civil War museum "represents a continuation of an investment that the state of Maryland has already begun," referring to both a heritage trail and the designation of Washington, Frederick and Carroll counties as a tourist area.
- Staff Writer Laura Ernde contributed to this story