WASHINGTON (CNN) -- Vice President Dick Cheney offered a sharp rebuke to congressional Democrats Monday, warning that a drawdown of forces in Iraq would invite more attacks on the United States.

Cheney's warning comes as Democrats are girding for a fight over more spending in Iraq -- a push planned even before President Bush's weekend request to deploy an additional 8,200 troops to Iraq and Afghanistan. House Democrats are leading a charge this week to set a deadline for withdrawal by August 2008.

In a speech to the American Israeli Public Affairs Committee, Cheney said even discussion of a withdrawal tells "the enemy to watch the clock and wait us out."

And an actual pullout would send an even worse message, he said.

"If terrorists conclude attacks will change the behavior of a nation, they will attack the nation again and again," he said. "The only option for our security and survival is to go on the offensive ... until our enemy is destroyed."

Cheney said morale among American soldiers in the Middle East is high, and asserted, "America is the kind of country that fights for freedom ... and we will prevail."

He brushed off criticism about faulty U.S. intelligence in the lead-up to the Iraq war and quoted Osama bin Laden as saying a U.S. defeat in Iraq would embolden al Qaeda and other terrorist groups.

"If you support the war on terror, then it only makes sense to support it where the terrorists are fighting us," he said.

Cheney's remarks were met with hearty applause from members of AIPAC, a pro-Israeli lobbying group. The vice president emphasized President Bush's ties to the Jewish nation, saying Israel has never had a stronger supporter in the White House.