Although the resolution against Rumsfeld is unlikely to be passed by the Republican-controlled senate, Democrats who have a strong chance of winning back control of at least one chamber of congress in November's mid-term elections, will use it to send a message that the administration's policies in Iraq are failing, according to Charles Schumer, a New York senator.
Schumer, chairman of the senate Democrats, told Fox news on Sunday: "It says that our policies are not going well.
"And the reason is not that we shouldn't fight a strong war on terror, but Rumsfeld's not doing a very good job of it."
Schumer said there was "a lot of sentiment" among senate Democrats to push for a resolution and noted that it was not just Democrats that have called for Rumsfeld to step down. Thomas H. Kean, a Republican candidate for the senate from New Jersey, did so on Saturday.
A similar resolution against the defence secretary is being considered by house Democrats.
Rumsfeld has said that his remarks made in a speech last week were misrepresented.
Mitch McConnell, the senate majority whip and a Kentucky Republican, told CBS's 'Face the Nation': "I think Secretary Rumsfeld has done an excellent job. He'll be remembered as one of the great secretaries of defence."
Howard Dean, chairman of the Democratic National Committee, said: "Of course Rumsfeld should resign. It is not smart to attack the majority of Americans who thought the war in Iraq was a mistake.
"Secretary Rumsfeld and Vice President Cheney have gone on television saying people who disagree with the president are essentially like Nazi appeasers. When you start attacking voters out of your frustration, that is not a good thing for winning elections."