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With President Bush making a surprise visit Tuesday to Iraq following that government's full organization and U.S. troops successfully targeting terror leader Abu Musab al-Zarqawi, both chambers of the U.S. Congress are preparing for an airing of differences on the strategy in Iraq.

The increasingly clear division between the two parties will be defined in a series of measures to be offered by Senate Democrats this week on setting withdrawal dates for U.S. troops.

Democratic Sens. John Kerry of Massachusetts and Russ Feingold of Wisconsin say they want most troops out by year's end. Senate Minority Leader Harry Reid and Sen. Carl Levin of Michigan, the ranking Democrat on the Armed Services Committee, say that deadline should be the end of 2007.

Click in the video box near the top of the story to watch a report by FOX News' Major Garrett.

For liberal activists, getting the troops out by the end of this year is the more attractive option, but the 2007 date is considered by several lawmakers the more reasonable and responsible alternative that keeps the pressure on the White House on withdrawals.

In the Kerry amendment, the U.S. Senate would call for some U.S. troops to stay in Iraq, but only those "critical to completing the mission of standing up Iraqi security forces." It would also call for "an over-the-horizon" troop presence to "prosecute the War on Terror and protect regional security interests."

According to the amendment being circulated by Levin, troops would be redeployed from Iraq to the Middle East region by the end of 2007. The amendment is to the Defense Authorization bill currently being considered on the Senate floor.

One senior aide to Reid said the language will "more tightly define" a phrase in the Iraq resolution passed last year that calls for 2006 to be a "year of significant transition in Iraq." In that vein, the amendment being considered in closed door meetings calls for the Bush administration to start to redeploy troops by the end of 2006.

"Getting out of Iraq will define success in Iraq," Sen. Chris Dodd, D-Conn., told FOX News as he expressed support for the amendment. He added that it's important to recognize that the amendment calls for "redeployment, not just withdrawal. It gets the neighbors involved...This is a region that requires a presence."

Sen. Dianne Feinstein, D-Calif., said she fully supports the Levin-Reid proposal, which will require the president to submit a report to Congress on how to implement this redeployment.

"It's been over three years. The time has come" to do something with the troops there, she said. Feinstein added that she's not worried that setting a timetable for troop withdrawal sends a dangerous message to the insurgency, as Bush and Secretary Don Rumsfeld have often said.

Dodd said it's too soon to get the troops out by year's end, but acknowledged that Democrats will not be unified on this issue. In the end, however, Democrats say they alone are moving the ball on troop withdrawals while Republicans stand pat.

Countering that they are hardly idling, Republicans argued Tuesday that every time a piece of news is reported from Iraq, either good or bad, Democrats manage to turn it into an opportunity to complain. Sen. John Cornyn, R-Texas, one of the Senate's strongest presidential supporters, said the latest proposals are no exception.

"We're going to have the annual cut-and-run amendments that are going to be offered by Senator Kerry and others, which are going to send exactly the wrong message but I think will demonstrate the difference in approach that the Democratic Party seems to have these days, that saying no to every positive suggestion, and even looking success in the face and snatching defeat out of the jaws of victory," Cornyn said.

Sen. Jeff Sessions, R-Ala., said he agreed that it's important for the Iraqi government to start taking responsibility for its future and "discussing a drawdown of American forces," but to set a timetable is inappropriate.

"I think it's irresponsible to demand a timetable for drawing down our forces because it must be based on the reality of what's happening in this country. And things go up and there are bad times, and you have to be able to adjust. And to make commitments that are unrelated to the situation is unwise," he said.

In fact, members in the House of Representatives on Thursday are devoting 10 or 12 hours of debate to an Iraq resolution written by GOP leaders that is basically a status quo policy position. It puts Iraq in the context of the War on Terror and says its wrong to set a troop withdrawal date.

Rules Committee Chairman David Dreier, R-Calif., said Tuesday the resolution and ensuing House debate would allow the House to express itself on Iraq and give members time to let their feelings be known about the war so far. Republicans want to draw Democrats out on the pullout question and show they remain unified on Iraq.

But House Minority Whip Steny Hoyer called the resolution "a political statement, not a policy statement." Asked what he thought of Democrats being deprived the right to offer an alternative, Hoyer told FOX News: "It tells me Republicans are afraid of ideas about Iraq."

Democratic Rep. Jim McGovern of Massachusetts also described his dissatisfaction with the debate.

"I don't want therapy. I want to change the policy. I think it's wrong," he said.

Rep. Tom Lantos of California, ranking Democrat on the House International Relations Committee, also complained that he was not consulted about the contents of the resolution, telling the committee he received the final version from a reporter. He branded the GOP rules for debate a "charade."

But Rep. Henry Hyde, chairman of the same committee, told members of the panel: "You win an election, you win the majority and then you set the policy and then we will complain."

On the substance, Rep. Duncan Hunter, chairman of the Armed Services Committee, defended the resolution, saying it was time for Congress to endorse what he called the "tough, hot, dusty, dirty, grinding process" of pacifying Iraq and stabilizing the new Iraqi government. Hunter said if Democrats disagree with the policy, they can say so during the debate.

Dreier added that Democrats have had ample time to offer amendments on troop withdrawals or reducing funding for the Iraq war on defense authorization and spending bills but chose not to do so. Republicans, he said, naturally concluded that Democrats had no consensus alternative to current policy in Iraq and therefore the GOP-drafted Iraq resolution should frame the debate.

Key House Democratic policymakers are meeting to come up with an alternative or coherent message on Iraq. They acknowledge that House Democrats have been divided over the best approach to seeing the situation in Iraq to its best conclusion.

Even as the chambers debate policy, lawmakers are still handing out cash for Iraq. An emergency supplemental bill that gives $66 billion to the wars in Iraq and Afghanistan as well as additional money to the Gulf Coast for Hurricane Katrina recovery was approved in the House and will be ready for a final vote in the Senate on Wednesday. That money does not show up on the annual accounting of deficit spending, but still shows up as part of the public debt

Sen. John McCain, R-Ariz., and many Senate Republicans are endorsing a change to that, backing a plan to pay for the Iraq war in the regular Defense Department budget.

"I'm in discussions with Senator Warner and with Senator Stevens to see if we can't get agreement, since everyone agrees that we should have a lot of this in the normal budgetary process so it can be examined by the authorizing committee," McCain said, referring to the Armed Services and Appropriations committee chiefs, respectively.

Republicans say they want to stop paying for the war through emergency spending bills that don't require budget offsets or tax increases to pay for the war. Recognizing the strain on the deficit, they say they now want the war to compete with regular government programs so that its importance can be demonstrated by forcing lawmakers to make difficult choices.

The White House apparently is okay with the decision, seeing future Iraq costs as being more manageable. It wouldn't otherwise endorse the budget change if it thought it would harm future funding.

FOX News' Major Garrett and Trish Turner contributed to this report.

Click in the video box near the top of the story to watch a report by FOX News' Major Garrett.