Republicans, changing course midway through a vote, tried to force Democrats into a debate on the resolution sponsored by longshot presidential candidate.
The anti-war Ohio Democrat, in his resolution, accused Cheney of purposely leading the country into war against Iraq and manipulating intelligence about Iraq's ties with al Qaeda.
The GOP tactics reversed what had been expected to be an overwhelming vote to table, or kill, the resolution.
Midway through the vote, with instructions from the GOP leadership, Republicans one by one changed their votes from yes - to kill the resolution - to no, trying to force the chamber into a debate and an up-or-down vote on the proposal.
At one point there were 290 votes to table. After the turnaround, the final vote was 251-162 against tabling, with 165 Republicans voting against it.
"We're going to help them out, to explain themselves," said Rep. Pete Sessions, R-Texas. "We're going to give them their day in court."
Democrats countered by offering a motion to refer the proposal to the House Judiciary Committee for further study, effectively preventing a debate on the House floor. That motion passed by a largely party-line vote of 218-194.
The White House, in a statement, said Democrats were shirking responsibilities on issues such as childrens' health insurance "and yet they find time to waste an afternoon on an impeachment vote against the vice president. ... This is why Americans shake their head in wonder about the priorities of this Congress."
Kucinich has long pushed for a vote to impeach Cheney, but has failed to win the backing of the Democratic leadership. After Kucinich introduced the resolution, House Majority Leader Steny Hoyer, D-Md., immediately moved to table it.
House Speaker Nancy Pelosi said "impeachment is off the table" and Congress is focused on responsibly getting U.S. troops out of Iraq, covering 10 million uninsured children and meeting national priorities long neglected by the Bush administration, said her spokesman Nadeam Elshami.
The resolution said that Cheney, "in violation of his constitutional oath to faithfully execute the office of vice president," had "purposely manipulated the intelligence process to deceive the citizens and Congress of the United States by fabricating a threat of Iraqi weapons of mass destruction to justify the use of the U.S. Armed Forces against the nation of Iraq in a manner damaging to our national security interests."
The 11-page resolution also charged that Cheney purposely deceived the nation about an alleged relationship between Iraq and al Qaeda and has "openly threatened aggression against the Republic of Iran absent any real threat to the United States."
House approval of an article of impeachment sends the issue to the Senate, which has the constitutional authority to try and, with a two-thirds vote, remove a person from office.