The Connecticut lawmaker also accused officials at the Defense Department of withholding information about the Iraq war from Congress.
"I am losing faith in how we are fighting this war," Shays, a longtime supporter of the conflict, said in an interview. "I believe we have to motivate the Iraqis to do more."
Shays said defense officials stopped cooperating with his congressional subcommittee after he proposed setting a timeline for troop withdrawals. Shays, who had previously opposed such a timeline, offered the plan in August following his 14th trip to Iraq since the war began.
Rumsfeld "simply is refusing to cooperate with a committee that oversees the Department of Defense," Shays said. "To me he has crossed the line."
"I think Donald Rumsfeld needs to step down," Shays said.
Several congressional Democrats have clamored for Rumsfeld's resignation, but it's rare for a lawmaker in President Bush's political party to argue that the Pentagon chief should step down. Republican candidate Tom Kean Jr., who is seeking a Senate seat in New Jersey, also has called for Rumsfeld's resignation.
Shays' opponent, Democrat Diane Farrell, has opposed the war and advocates an exit strategy for U.S. troops. Farrell lost to Shays by 4 percentage points two years ago.
Farrell's campaign pointed out that she has been calling for Rumsfeld's resignation for months and said this is just the latest change in Shays' position.
"He has supported the war from Day One," said Farrell campaign spokeswoman Jan Spiegel. "He has voted to give the president a blank check."