Appearing on Face the Nation, Senate minority leader Mitch McConnell, R-Ky., said that members of his party believe judgment of the surge's effectiveness should be withheld until Ambassador Ryan Crocker and Gen. David Petraeus, the top U.S. commander in Iraq, deliver a progress report to Congress.
"I think the proper time to really make a serious evaluation of the direction we ought to head is in September," McConnell said.
Crocker, the U.S. Ambassador to Iraq, and Defense Secretary Robert Gates have said that the outlook for Iraq is a mixed picture but is not hopeless. Polls show, however, that public support for the war among Americans is dwindling, and violence in Iraq shows no signs of slowing.
Democratic Senator Carl Levin, the Chairman of the Armed Services Committee, said now is the time to go a different direction.
Although President Bush vetoed legislation passed by congressional Democrats setting a timetable for withdrawal, Levin said his party will try again to begin an American troop withdrawal. This time, he said, Democrats will be successful because they have support from more frustrated Republicans.
"We are going to be offering an amendment which will, in one form or another, set a timetable for the reduction of American troops starting in about 120 days," Levin told Bob Schieffer. "We have got to change this course. We have got to change the Iraqi mentality [of] thinking that they have got some kind of an open-ended commitment, which is what the president promised them a few months ago."
McConnell said he expects a change in policy to come, but he said he wants to see how the surge strategy works.
"I don't think we'll have the same level of troops, in all likelihood, that we have now," he said. "The Iraqis will have to step up, not only on the political side, but on the military side, to a greater extent."
It is the Iraqi government, McConnell said, that deserves the lions share of the blame for the chaos in Iraq.
"The Iraqi government, so far, has been a big disappointment," he said. "They've not done the things that they know they need to do to hold their country together."
But, former Congressman and chair of the Iraq Study Group, Lee Hamilton, told Schieffer that U.S. forces can't withdraw from Iraq until Iraqi forces can take over responsibility for security.
"Our primary mission today is the surge," Hamilton said. "We're not going to get out of Iraq unless we train better than we have the Iraqi forces and let them take over some of the responsibilities we now have."
McConnell said he thinks there is growing support for the recommendations made by Hamilton and James Baker in the Iraq Study Group report.
Released last year, the report stressed more dialog with regional powers like Syria and Iran while maintaining a strong military presence at Iraq's borders. It recommended against a troop surge.
"There is still no military solution to Iraq," Hamilton said on Face the Nation. "The military plays a hugely important role, but you must have vigorous, robust efforts to get a national reconciliation."
Both Levin and McConnell said that the Iraqi government has failed to live up to its part of the bargain and hasn't assumed control of the country.
"What's required here is for the President of the United States to tell the Iraqi leaders that we're going to begin to reduce our troops as the message to them that the responsibility for their own country is in their hands, not ours," Levin said.
The Iraqi congress is also thinking of taking a two-month summer vacation.
"You cannot do that while our troops are dying and being wounded and your troops are dying and being wounded and your people are being blown up," Levin said.