The strike would be embarrassing for Gordon Brown and the Labour Party, trailing in the opinion polls.
Unite is Labour's largest financial backer and the party's strong union ties go back to its foundation in 1900. Unite's political director is Charlie Whelan, Brown's former spokesman.
Conservative leader David Cameron has accused Brown of failing to stand up to the union and compared the situation to the 1970s, which saw periods of industrial unrest under Labour.
"When the crunch comes, he can only act in the union interest, not in the national interest," Cameron said this week.
Business Secretary Peter Mandelson said the strike was "quite disproportionate" and he rejected suggestions the union had influenced the government's response.
"Given the government's very clear position on this dispute, anyone would be able to judge that Unite or anyone working for this union is not dictating our policy," he said.
BA hopes to fly at least 60 percent of customers booked for the March 20-22 period after it trained staff to provide cover.
(Editing by Elizabeth Fullerton)