Republican and Democratic members of Congress criticized the embattled Pentagon chief on Sunday for not signing the letters himself all along.
"My goodness, that's the least that we could expect of the secretary of defense, is having some personal attention paid by him," said Sen. Chuck Hagel, R-Neb., noting that President Bush signs such letters himself.
"If the president of the United States can find time to do that, why can't the Secretary of Defense?" asked Hagel, a Vietnam veteran, on CBS' "Face the Nation."
Hagel joined other prominent Republicans and said he had no confidence in Rumsfeld.
"I find it astounding. ... Things are worse than they've ever been" in Iraq, Hagel said. However, he did not say Rumsfeld should step down. He said it was up to President Bush whether to replace Rumsfeld.
Earlier in the week, Sen. John McCain said he had "no confidence" in Rumsfeld. Sen. Trent Lott said that Rumsfeld did not listen to uniformed officers and that Mr. Bush should make a change at the Pentagon in the next year or so.
However, on Sunday two leading Republican senators expressed reluctance that the White House replace Rumsfeld.
The chairman of the Senate Armed Services Committee said a change would be too disruptive, given the elections scheduled in Iraq for Jan. 30. Sen. John Warner also said the administration was dealing with the missteps that have occurred in the aftermath of the U.S.-led ouster of Iraqi President Saddam Hussein.
"We should not at this point in time entertain any idea of changing those responsibilities in the Pentagon," the Virginia senator said in a broadcast interview.
The Bush administration's biggest mistake in Iraq was the rapid disbanding of military forces "and not trying to maintain some of it in place to have continuity and to rapidly put together a security force," Warner said.
Sen. Richard Lugar, chairman of the Senate Foreign Relations Committee, added, "We really can't go through that ordeal" now of finding a successor. Rumsfeld "should be held accountable, and he should stay in office," said the Indiana senator.
Sen. Susan Collins, a Republican from Maine, is outraged that thousands of Humvees have yet to be outfitted with upgraded armor, despite months of prodding.
Critics also charge Rumsfeld misjudged the troop strength needed in post-war Iraq- and then stubbornly refused to re-consider.
They fault his handling of the Abu Ghraib prison scandal, and a sweetheart deal on his watch to lease Boeing aircraft as air force tankers.
Rumsfeld, who agreed to Bush's request this month to stay in the Cabinet during the president's second term, won a vote of confidence from the White House on Sunday.
"Secretary Rumsfeld is doing a spectacular job," said the president's chief of staff, Andrew Card, in a broadcast interview.
"The president has provided good direction for our military, and Secretary Rumsfeld is transforming our military to meet the threats of the 21st century," Card said.
While security remains a problem in Iraq, Card said the growing economy and the establishment of the educational and electrical systems in the country were positive developments.
"There are no guarantees, but we'll work hard to provide security," for the elections, Card said. "It'll be a wonderful success story."
Card said Rumsfeld has a good relationship with Congress and "knows the budgets that are needed to fight the war."
Rumsfeld will soon have to ask Congress for another $75 billion to $100 billion dollars to pay for the war in Iraq.
At the same time, Rumsfeld also must oversee the transformation of the military "to meet the threats of the 21st century, and that transformation is controversial," Card said.
"I'm sure that some of the people that are stuck in the past don't want to see the military transformed."