The particularly harsh exchange came just hours afterthe latest war spending bill taking shape in Congress, which includes a timetable for withdrawing from Iraq.
The vice president was so angry at Reid that he did something he almost never does, reports CBS News correspondent Sharyl Attkisson. Cheney stopped to talk to reporters after his weekly meeting with Senate Republicans.
"Some Democratic leaders seem to believe that blind opposition to the new strategy in Iraq is good politics," Cheney said. "Sen. Reid himself has said that the war in Iraq will bring his party more seats in the next election."
"It is cynical to declare that the war is lost because you believe it gives you political advantage," Cheney said.
Cheney said he felt compelled to make a statement in front of cameras to express his personal frustration with Reid, D-Nev., after the Senate majority leader told reporters last week the war was lost. Cheney's remarks also showed the high stakes involved for the White House in trying to stave off Democratic efforts to end the war.
While Bush has enough Republican votes to sustain his veto, Democrats say they have public opinion on their side and that will eventually force Bush to change.
"This isn't a political issue," said House Speaker Nancy Pelosi, D-Calif. "I respect where the president is coming from on this. I wish he would respect where we are coming from, which is a reflection of where the American people are coming from."
Reid shrugged off Cheney's remarks — but with his own dig at the vice president.
"I'm not going to get into a name-calling match with the administration's chief attack dog," he said.
The $124.2 billion legislation would continue to fund the war in Iraq but also would require that troops begin pulling out by Oct. 1 or earlier if the Iraqi government does not make progress in tamping down sectarian violence and forging political agreements. The bill ultimately sets a nonbinding goal for combat operations to end by April 1, 2008.
"It's a good piece of legislation," Reid said. "I would hope the president would stop being so brusque and waving it off. This is a bill that is good for the troops. It's good for the country."
With Democrats expecting to send Mr. Bush the final bill as early as next week, the president stood firm Tuesday against any measure that would set a timetable for withdrawal.
"They chose to make a political statement," he said. "That's their right, but it is wrong for our troops and it's wrong for our country. To accept the bill proposed by the Democratic leadership would be to accept a policy that directly contradicts the judgment of our military commanders."
House Majority Leader Steny Hoyer said Democrats will ignore the veto threat and send the bill to Mr. Bush in the hope that he will have a change of heart. But, Hoyer added, they don't expect it.
"He will do with it what he will do," said Hoyer, D-Md. If Bush vetoes the measure, Democrats will consider their next step and try to bring Republicans on board.
"My intuition tells me there are an awful lot of members of the president's party who have great concerns about simply staying the course," Hoyer said.
Mr. Bush said U.S. troops should not be caught in the middle of a showdown between the White House and Congress.
"Yesterday, Democratic leaders announced that they planned to send me a bill that will fund our troops only if we agree to handcuff our generals, add billions of dollars of unrelated spending and begin to pull out of Iraq by an arbitrary date," Bush said on the South Lawn.
He said the bill would mandate the withdrawal of troops despite the fact that the top U.S. commander in Iraq, Gen. David Petraeus, has not yet received all the reinforcements he has said he needs to secure Baghdad and the troubled Anbar Province.
Democrats have argued that the election that left them in control of Congress was a referendum for a change of strategy in Iraq. Mr. Bush used the same election results to argue his point.
"The American people did not vote for failure," he said. "That is precisely what the Democratic leadership's bill would guarantee."
Petraeus and other top defense officials on Wednesday will try to persuade lawmakers in a private briefing not to set a timetable.
Under the bill, U.S. forces could remain in Iraq after the 2008 date, but would be restricted to three non-combat missions: protecting U.S. personnel and facilities, engaging in counterterrorism activities against al Qaeda and other similar organizations, and training and equipping Iraqi forces.