With lawmakers from the opposition Democratic Party in control of both the House of Representatives and the Senate, spirited debate can be expected.
Many legislators face growing pressure from their constituents to start bringing U.S. soldiers home, so the testimony is seen as a potentially decisive moment in the U.S. political debate on Iraq.
Reports say Petraeus and Crocker are expected to defend President George W. Bush's "surge" policy of increasing the number of U.S. troops in Iraq, and advise against any major decrease in forces at the current time. They are expected to describe uneven military progress, and unsatisfactory political progress among Iraqi leaders, but to ask for more time to seek success.
Almost 170,000 U.S. Troops In Iraq
When U.S. President George W. Bush announced the surge in January, he said he would send about 21,000 additional troops to Iraq. That number has now grown to 30,000 extra soldiers, bringing total U.S. forces in Iraq to almost 170,000 troops.
The strategy was designed to help stabilize Iraq long enough for its government to make political progress in reconciling the country's Sunnis and Shi'a.
Congress, which decides on funding for the war, has set 18 benchmarks for measuring progress in Iraq. They include military goals, such as whether Iraqi forces are ready to take over from U.S. troops, as well political goals, such as whether the Iraqi government has made progress toward political reconciliation.
Members of the House of Representatives' Foreign Affairs Committee are expected to quiz Petraeus and Crocker at length about whether those goals are being met.
Too Much Focus On Troop Reductions
Anthony Cordesman, a former Pentagon and State Department analyst, now studies global strategy at the Center for Strategic and International Studies, a private policy-research center in Washington.
He says the problem is that too many observers are focusing exclusively on troop reductions, and thinks they should balance that with other factors, including the Iraqi government's efforts to reconcile the country's factions.
"If you do have political conciliation, even if it's only a serious beginning, then the pressure on U.S. troops is going to go way down and the critics of the war are going to lose, really, the fundamental issue." -- Cordesman
So far, it isn't clear whether that government can hold together, either under the current prime minister, Nuri al-Maliki, or under some other leader, according to Cordesman. But he adds that if there is some political progress, U.S. troops will be able to do their job better.
"If you do have political conciliation, even if it's only a serious beginning," Cordesman says, "then the pressure on U.S. troops is going to go way down and the critics of the war are going to lose, really, the fundamental issue, which is not U.S. troop levels but the fact that we're fighting without watching an Iraqi government create the kind of national unity and conciliation that offers a clear reason to sustain our presence in Iraq."
Ultimately, Cordesman believes Congress will vote on continued funding for Iraq in accordance with the wishes of the American people. And he believes voters won't judge the war on just one or two issues, such as troop levels or reports of political progress.
Working With Sunni Sheiks
One of the highlights of all the early evaluations so far is that Sunni sheiks in Al-Anbar Governorate, west of Baghdad, are now thoroughly embittered about Al-Qaeda in Iraq, with whom they were once allied. Recently, they've been working with U.S. forces against Al-Qaeda in Iraq.
Bush's surprise visit to the governorate on September 3 highlighted this shift.
Michael O'Hanlon, a foreign-affairs specialist in Washington at the Brookings Institution, says it's too early to tell whether this alignment can last.
He suggests the Al-Anbar Sunnis may eventually end it, perhaps not trusting the Americans to intercede on their behalf before the Shi’ite government. On the other hand, if the alliance lasts, it may rankle the country's Shi’ite leadership.
Either way, O'Hanlon concludes, the United States faces "huge challenges."
"I think the most important thing to say is that [the U.S.-Sunni collaboration] will not continue indefinitely in the current form," O'Hanlon says. "You'll have to have a different alignment of interests -- of somewhat different interests -- for it to be sustainable. And I think, again, we come back to the crucial, central question of: Can you get the Sunni and Shi’a in Iraq to begin to at least make partial accommodation with each other? If you can, then I believe this alliance with the Sunni tribes can become durable. If not, we're probably going to lose somebody [as an ally] -- either the Sunnis or the Shi’a -- over the coming months."
Political Progress Crucial
O'Hanlon says there's also no way of telling whether the United States can parlay its current relations with the Al-Anbar Sunnis and the Shi'a who control the government into improved relations between the two bitter enemies.
O'Hanlon is certain of one thing, however. Continued progress by U.S. forces can't make up for a lack of political progress by Iraq's leaders.
"We're in a world where the United States has to start getting out because we don't have enough forces to sustain this," O'Hanlon says, "and also we aren't really universally appreciated inside Iraq, and it causes us a lot of problems to be there. So in that situation, you need the Iraqi population to be able to trust the Iraqi security forces, and you need the security forces to be dependable, even when they're made up of a mix of different sectarian groups."
To O'Hanlon, the United States simply isn't on a course to true victory in Iraq. But he believes it can achieve success, which he defines as making Iraq stable enough so that U.S. forces can be withdrawn altogether.
"If Iraq can at some level hold together and not become a state that hosts Al-Qaeda, or builds nuclear weapons, or attacks its neighbors, or massacres its minorities," O' Hanlon says, "then I think we can tolerate almost anything else. We can tolerate benign dictatorship. We can tolerate an Iraq that leans toward Iran. We can tolerate an Iraq that leans toward Syria. As long as we don't have an active promoter of terrorism, or an active pursuer of nuclear weapons, or a country that either attacks its neighbors or massacres its minorities, I think we can tolerate virtually any other outcome."
The United States, he says, can't realistically set its goals any higher than that.
Read the full transcripts of RFE/RL's interviews with Anthony Cordesman and Michael O'Hanlon.