The government has been forced onto the defensive over its deployment of 2,000 troops in Afghanistan and the enlargement of a US military base at Vicenza in northern Italy.
Both policies are strongly opposed by the left, which is part of Prodi's multi-party government.
D'Alema said that to go back on the approval that the prime minister gave last month for the base enlargement would be a "hostile act" toward the United States.
More than 80,000 people took part in a rally last Saturday in Vicenza against the enlargement.
Prodi's coalition narrowly beat Silvio Berlusconi's conservatives in a general election last year.
His fragile ruling coalition, which ranges from Catholics to communists, has only a one-seat majority in the senate but in the past had managed to win majority support despite divisions by calling confidence votes.