Even so, the Mahdi fighters seemed to hold their ground. Witnesses said that from the worn, closely packed brick buildings of one Mahdi stronghold, the Hayaniya neighborhood, Mahdi fighters fired mortars, rocket-propelled grenades, automatic weapons and sniper rifles at seemingly helpless Iraqi Army units pinned on a main road outside, their armored vehicles unable to enter the narrow streets.
Unfortunately the Times (along with other outlets) seem to accept at face value the claims by Iraqi and American officials that the operation is intended to root out "militias" in general, and is not aimed specifically at the Mahdi Army (this CNN article is much better at explaining what's going on.) It's only later in the article that the Times clarifies the situation:
Though American and Iraqi officials have insisted that the operation was not singling out a particular group, fighting appeared to focus on Mahdi-controlled neighborhoods. In fact, some witnesses said, neighborhoods controlled by rival political groups seemed to be giving government forces safe passage, as if they were helping them to strike at the Mahdi Army.
Also mentioned later in the article is the fact that only Mahdi Army members seem to be reacting negatively to the assault by fighting back in other parts of Iraq (like Sadr City) a fact that seems to belie the claim that the operation is aimed at all the Shiite militias in Basra. I don't know why it's so hard to make this rather obvious fact clear at the outset of the article, but then I'm not a journalist or newspaper editor so what do I know? In addition, there are scattered reports in the Arabic media that members of the rival militia the Badr Brigade are rushing to fight alongside Iraqi security forces against the Mahdi Army, reports that make it quite clear that this operation is not about imposing security on Basra...except in the sense that the city will belong to Fadila and SIIC afterwards.
Unknown bombers also blew up one of Iraq's major oil pipelines that runs south of Basra. Sadr has responded to the attacks by continuing to call for civil disobedience only, even as some of his more fervent followers are busy rocketing and shelling the Green Zone and major clashes between militia members and security forces continue in Baghdad, Kut (which the Mahdi Army has apparently taken over) and the cities surrounding Baghdad, clashes that make it quite clear that while the cease-fire between Sadr and U.S. and Iraqi forces may technically still be in effect, it is in reality quite over. American forces have thus far declined to intervene except to launch supporting airstrikes, but it's impossible to know how long that restraint can last when the Mahdi Army is busing fortifying Sadr City.
UPDATE: Of course, American officials are selling this offensive as a sign that the Iraqi forces can stand up on their own (that would be the "silver lining" that we keep hearing about. ) That spin-dubious as it is, at best-may yet come back to bite them if Iraqi forces prove to be incapable of pacifying Basra and eliminating the Mahdi Army.
UPDATE II: One of the reasons casual followers of the situation in Iraq may not know what the hell is actually going on in the country and are surprised by situations like the Basra offensive is because of attitudes like those possessed by (the late) Peter Jennings, who felt compelled to apologize when on the night of the opening of the invasion of Iraq he accidentally interviewed Iraqis who weren't that pleased by our forth-coming presence in their country. Sadly, as Greenwald documents, this attitude has not changed as much as it should have over the last five years.
UPDATE III: Dan Froomkin at the Washington Post with more on the Bush administration's spin. And via Froomkin, this article in Time from Darrin Mortenson which highlights why Bush administration officials are secretly hoping like hell that the Iraqi security forces can destroy the Mahdi Army in Basra (even as they assure us that they will, of course.) If they fail, the already short-handed U.S. military may have to clean up after them by getting back into the middle of the Shiite civil war (you wouldn't even know the British remain in Basra, as they have no intention of reappearing from their fortified airport.) Honestly, it's hard to say where this is going. It's impossible for me to imagine Maliki, who swears the Iraqi forces will fight until the end, backing off until the Mahdi Army's influence in Basr is substantially destroyed. But how long will Sadr sit claiming that the cease-fire is still in effect? More importantly, how long will his followers in other Mahdi Army strongholds in the South and in Baghdad allow him to wait? How will they respond if the fighting continues or worsens? And what happens if the security forces fail to clear the Mahdi Army out of Basra? Where is the resolution to all of this? I've come across no commentary online, no matter how well-informed, that can offer an answer.
UPDATE IV: Maliki is betting on crushing the Mahdi Army in Basra, but as the offensive there stalls the Times reports that the Mahdi Army is taking over portions of Baghdad with relative ease (via Balloon Juice commentator wwz.) There is still no sign that U.S. forces plan to engage them and it will probably remain that way until a) Sadr calls off the cease-fire or b) the security situation grows so poor that the must intervene regardless of Sadr's official pronouncements.
UPDATE V: Here's the invaluable Marc Lynch with his summary of the various theories about what's going on with Basra right now:
So you can add the  "Iran is liquidating its no longer useful proxies" theory (which would fit this general line of speculation about Iran's doubts about Sadr and preference for the simultaneously-US backed ISCI) to the generally most prevalent (in the Iraqi and Arab, not just Western, media)  "Maliki and ISCI are liquidating their more popular rivals ahead of the provincial elections" theory; the optimistic  "Sadr has lost power and now's the time to take him out" theory (thus far not borne out by the course of the fighting, but who knows - it's early, or it could be a miscalculation);  Maliki's own "it's time to establish state sovereignty over a 'lost' province" theory (which Bush, of course, has embraced, and is supported by the reporting that the Iraqi Army began its preparations for the attack months ago; but then why isn't he taking on the other militias and warlords? and why would he start now, and in Basra?); and  Reidar Visser's "Maliki is trying to build a power base in the Iraqi Army" theory. [note: numbers added to make Kevin Drum happy.]
Which is it? Who knows? But you can probably be safe in saying that #3 is wrong.
UPDATE VI: In response to the scattered fighting and protests in Baghdad, Iraqi security forces have instituted a curfew to begin Thursday night (Baghdad time.) President Bush accuses Congress of "hectoring" Iraqi leaders in response to the slow pace of political reconciliation. CNN Baghdad correspondant Michael Ware believes that this is part of an effort by Iran to reign in Sadr and diminish his influence against their preferred Shiite parties Dawa and SIIC. He's not the only one who thinks so, if you see the Lynch post I link to above. The questions remain of course: how serious is Maliki about carrying this operation out to the end? And how long does Sadr sit on the cease-fire?
UPDATE VII: One more link on the battle for Basra. As noted above the offensive appears to have stalled, but this AP story reports widespread dissatisfaction among Iraqi military and security personnel, including complaints about how well-armed the Mahdi Army is in comparison, reluctance to fight other Iraqis, and and outright defections and desertions.