White House officials have met several Republican senators in an effort to shore up support over Iraq.
Growing numbers of US lawmakers are calling for change on Iraq
National Security Adviser Stephen Hadley visited Congress as two more Republicans joined the ranks of those calling for a phased troop withdrawal.
US President George W Bush says he will again veto any bill passed by Congress that sets a timetable for withdrawal.
The White House must release by Sunday an interim report detailing progress in the current "surge" operation in Iraq.
The report is expected to show that the Iraqi government has made only limited progress in meeting political and military objectives set out by the US Congress.
Speaking in Ohio on Tuesday, Mr Bush said he understood how hard the Iraq war was for the US.
But he added that Congress must give his surge plan, under which 30,000 extra troops have been deployed in Iraq, time to work.
He urged lawmakers to wait for the full report, due to be delivered in mid-September by the head of US forces in Iraq, General David Petraeus.
Republican Senators Olympia Snowe and Elizabeth Dole have become the latest to add their voices to those demanding a new plan for Iraq.
Democrats want a timetable for withdrawal or a change in the focus of the US mission from combat to counter-terrorism and the training of Iraqi forces.
In order to overturn the threatened presidential veto, they would need to muster a two-thirds majority in both the House and the Senate.
Republican Senator Olympia Snowe, from Maine, told Reuters news agency there was growing impatience in Congress for a change in policy.
By September there might be sufficient Democrats and disaffected Republicans for a withdrawal measure to pass, she said.
Fellow Republican Elizabeth Dole, a senator from North Carolina, also challenged the Bush administration's approach.
"Simply put, our troops have been doing a great job, but the Iraqi government has not," she said.
"Our commitment in Iraq is not indefinite, nor should the Iraqi government perceive it to be. It is my firm hope and belief that we can start bringing our troops home in 2008."
Democrats in the House of Representatives - where they hold a strong majority - are meeting on Wednesday to discuss a proposed bill requiring troop withdrawal to begin within 120 days of it being passed and to be completed by 1 April 2008.
Gen Petraeus has said it is too early to assess if the surge is working
Democratic leaders say a vote on the legislation will be held this week and that they expect the measure to pass the House.
Democratic House Speaker Nancy Pelosi said: "The American people want Congress to bring our troops home, refocus our efforts on fighting terrorism, and hold the Bush administration accountable."
Earlier this week, Gen Petraeus said it was too soon to tell if the surge is working and told the BBC that fighting the insurgency was a "long term endeavour" which could take decades.
Iraqi leaders have expressed alarm at the prospect of a premature US withdrawal, saying it could cause the country's disintegration.