"To oppose everything while proposing nothing is irresponsible," Mr. Bush said.
But, Mr. Bush's challenge sounds hollow. The president told Scott Pelley in an exclusive interview to air on 60 Minutes this Sunday that he will go ahead with his plans to increase troops in Iraq regardless of whether Congress tries to stop him.
"I made my decision, we're going forward," Mr. Bush said.
In his latest pitch to lawmakers and the American people, Mr. Bush said the United States will keep the onus on the Iraqi government to take charge of security and reach a political reconciliation. He countered Democrats and his fellow Republicans who argue that Mr. Bush is sending 21,500 more U.S. troops into Iraq on the same mission.
"We have a new strategy with a new mission: Helping secure the population, especially in Baghdad," Mr. Bush said in his weekly radio address. "Our plan puts Iraqis in the lead."
Democratic leaders in the House and Senate intend to hold votes within a few weeks on Mr. Bush's revised Iraq policy. The nonbinding resolutions would be one way to show their opposition to any troop buildup and force Republicans to make a choice about whether they support the president's plan.
Rep. Tim Walz, D-Minn., said that he, along with most Democrats and an increasing number of Republicans, believe sending more troops compounds a bad situation. Walz, a veteran of the war in Afghanistan, said diplomatic and political solutions are needed, not more troops.
"Before moving forward with this escalation, we owe it to these troops, to their families, and to all Americans to ask the tough questions and demand honest answers about this policy," Walz said in the Democrats' Saturday radio address.
"Is there a clear strategy that the commanders on the ground believe will succeed?" Walz said. "What are the benchmarks for success, and how long does the president believe it will take to achieve them? Is this a policy that will contribute to the America's security in the larger war on terror, or distract from it?"
Senate Minority Leader Mitch McConnell, R-Ky., has charged that what Democrats really want to do is cut off funding for the troops. Democrats deny that.
"Members of Congress have a right to express their views, and express them forcefully," Mr. Bush said. "But those who refuse to give this plan a chance to work have an obligation to offer an alternative that has a better chance for success."
In his radio broadcast, Mr. Bush replayed the highlights of his Wednesday night address to the nation.
He said the 21,500 troops being sent to Baghdad and Anbar province, a base for al Qaeda, have a changed mission.
"This time there will be adequate Iraqi and U.S. forces to hold the areas that have been cleared," Mr. Bush said.
Mr. Bush said Iraqi Prime Minister Nouri al-Maliki has pledged that political sectarian interference with security operations will not be tolerated. "This time, Iraqi and American forces will have a green light to enter neighborhoods that are home to those fueling sectarian violence," he said.
The president also said the United States will hold the Iraqi government to its pledge to take responsibility for security in all of Iraq's provinces by November, pass legislation to share oil revenues among all Iraqis and spend $10 billion of its own money on reconstruction that will create new jobs.
"The Iraqi government knows that it must meet them, or lose the support of the Iraqi and the American people," Mr. Bush said.