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Watch McConnell’s comments Friday.

WASHINGTON (CNN) – The top Republican in the Senate made clear Friday he and the GOP membership expect a thorough assessment of progress in Iraq by mid-September, as planned.

Feeling political pressure from national polls, and his own jittery members, Mitch McConnell of Kentucky told reporters, "There may be various generals or various politicians who want to mention some other key time," for measuring how things are going, but "the key time for the vast majority of my members is September. And it certainly is for me."

In a news briefing Thursday, Lt. Gen. Raymond Odierno, deputy to the commander of U.S. forces in Iraq, indicated it would take "at least until November" to truly assess how the troop increase was working.

But Odierno issued a statement Friday saying he had not meant to indicate there is an effort "to push our reporting requirement beyond September."

"My reference to November was simply suggesting that as we go forward beyond September, we will gain more understanding of trends," he said.

McConnell, asked by reporters if he would be willing to wait until November, said no.

The Senate minority leader, who has expressed some concerns about progress in Iraq, described himself as "confident in saying for most of the members of my conference, September's the month we're looking to" for reports from the top commander in Iraq, Gen. David Petraeus, and Ambassador Ryan Crocker.

Still, McConnell took time to criticize Democrats for pushing for withdrawal timeframes in Congress before the reports are delivered. "I'm interested in knowing what the actual facts are; what General Petraeus has to say about the mission," he said.

White House spokesman Tony Snow downplayed Odierno's comment, telling reporters Friday that Petraeus "has already said he's going to be making recommendations in September ... and he will do it."

Snow added the administration will be looking for "a demonstration that the surge is working."

– CNN Radio's Bob Costantini