"They ought to put a sign on the [Republican] National Committee doors that says 'Closed for Repairs' until New Year's Day next year and spend that time going over ideas and positive agendas," the former Senate majority leader told "Fox News Sunday."
"Reagan wouldn't have made it. Certainly [Richard] Nixon couldn't have made it, because he had ideas. And we might have made it," the former Kansas senator said of his vintage of Republican, "but I doubt it."
"I just consider myself a Republican -- none of this hyphenated stuff," he said. "I was a mainstream conservative Republican, and most people are in that category."
Reagan was president from 1981 to 1989 and is widely credited with generating an ideological renaissance on the American political right. Nixon was president from 1969 to 1974 and is the only U.S. president to resign the office.
Dole, who turns 90 July 22, described Nixon as "brilliant" but a "criminal" who "could have been a great president -- he just threw it away."
Dole, in the Senate from 1969 to 1996 and the House from 1961 to 1969, criticized Washington's divisive standoff.
"It seems to be almost unreal that we can't get together on a budget or legislation," he said.
Those in office during his time "weren't perfect by a long shot, but at least we got our work done," he said, adding the Senate filibuster, used to prevent a measure from being brought to a vote, was being abused, "no doubt about it."
But Republican lawmakers aren't the only ones at fault for Washington's dysfunction, Dole told the program.
"The American people ... are partly at fault," he said.
Voters overwhelmingly say in opinion surveys they want spending cuts, Dole said, but they want those cuts only to apply to others.
"If you leave me, exempt me, I'm all for you," he said, referring to voters voicing support for fiscal conservatives.
"But if you cut something they have an interest in, they're over you like a wet blanket," Dole said. "They surely don't want to cut Medicare or Social Security."
Dole, who was the 1996 Republican presidential nominee who lost to incumbent Bill Clinton, also criticized President Barack Obama for Washington's deterioration, saying he hasn't worked closely enough with Congress to solve the country's problems.
"I'm not a critic of the president, but I think one mistake he's made was not getting together more with Congress earlier on, in his first administration," Dole said.
"There's nothing like knowing the person you're talking to on the telephone if you've had an opportunity to sit down with that person and visit, not about anything, but just visit," he said.
He called Obama "very articulate," but said, "As a president, he lacks communication skills with his own party, let alone the Republican Party. And he's on the road too much."