The government has refused to stump up more cash to help Bletchley Park stay afloat until the museum can support itself.
In a debate on Tuesday in the House of Lords, the chamber was told funding is needed to help keep the site financially viable while restoration work to the home of the World War II codebreakers is carried out.
During the session, Labour peer Baroness McIntosh of Hudnall petitioned the government for more money in the House of Lords.
"The fundraising effort is going pretty well, as is work to improve both the buildings and museum facilities. Visitor numbers are rising very rapidly and it will be self-sufficient once capital building work is completed. They are suffering considerable difficulty in continuing in the interim," Baroness McIntosh said.
"Could he [the government spokesman Lord Davies] encourage his friends at the Department for Culture, Media and Sport to reconsider their willingness to support this project?" she asked.
Lord Davies of Oldham, the deputy chief whip of the House of Lords, rejected McIntosh's call for government funding, adding there has already been substantial support for restoration work from English Heritage and Milton Keynes Council, which have donated a total of £930,000 between them towards restoring the manor house and general site improvement.
"Although I cannot say in the affirmative to her [McIntosh's] suggestion, the department is all too aware of the importance of ensuring support for such an historic site," Lord Davies said.
Other Lords echoed Baroness McIntosh's calls for more government cash for Bletchley, which was credited with planting the seeds of "the computer industry in this country" by one peer.
Lord Davies also rejected the suggestion that Bletchley should be associated with the Imperial War Museum to recognise the importance of its role in cracking codes used by the Nazis during World War II.