BEIRUT, Lebanon — Fighters loyal to the Islamic State of Iraq and al-Sham (ISIS) have at times been as close as six miles to Baghdad, according to Iraqi and Kurdish commanders interviewed by The Daily Beast. But the Iraqi capital may well be “a city too far” for this ferocious al-Qaeda offshoot that is determined, as its name says, to establish a state of its own.

While there’s no solid consensus among intelligence analysts in the region about ISIS’s precise strategy, several interviewed in recent days say the jihadists are likely to launch demoralizing commando raids and a suicide bombing blitz in Baghdad, probably timed to coincide with the arrival of the main contingent of US military advisers. (An advance guard arrived Tuesday.)

The Americans presumably will make the defense of the capital a priority, but that may be precisely what ISIS hopes they will do, because it has other interests. “The priority, I think, for ISIS is to build their Islamic State straddling the Syria-Iraq border – that is their ultimate objective—and trying to capture Baghdad would be too big for them to accomplish; it could also sidetrack them,” says a US intelligence official based in the Middle East who is closely monitoring ISIS.

ISIS has not picked difficult battles. It has calculated carefully where it could move with the biggest impact and the least resistance. Mosul was not Stalingrad, holding out against a powerful siege; it was more like Copenhagen in World War II, folding without a fight.

A concerted ISIS campaign to capture Baghdad would no doubt trigger greater military reaction from the Iranians -- key backers of the Shia-dominated government of beleaguered Prime Minister Nouri al-Maliki – who already have sent members of their Revolutionary Guard and military supplies to bolster Iraqi security forces. The Iranians reportedly are flying surveillance drone flights on behalf of Maliki’s government as well.

Such attacks as do take place in and around Baghdad will likely aim to sow political discord and fan sectarian divisions, keeping Maliki’s government wrong-footed and on the defensive. Iraqi troops and allied Shia militiamen are holding a line north of Baghdad and trying to establish what army commanders call the Baghdad Belt around the capital. But they are making little headway mounting an offensive, relying on instead on the spotty use of airpower to take the fight into ISIS territory.

Abu Bakr al-Baghdadi and other ISIS leaders have made clear their ambition to establish a caliphate stretching from Aleppo in Syria right across northern and western Iraq. “ISIS is not only talking the talk about establishing an Islamic state, it is walking the walk,” jihadist expert Aaron Zelin notes in a research paper on the group released Thursday by the Washington Institute for Near East Policy, a D.C.-based think tank.

“Further, the reality of a proto-state and ISIS’s willingness to try to govern—this khilafa project, as many within the group call it—is quite appealing to jihadists,” says Zelin. It is helping to attract recruits and undermine the standing of al-Qaeda, whose leadership disowned ISIS earlier this year, partly over its state-building aspirations.

On Baghdad, Zelin told The Daily Beast that ISIS has always had a presence in the capital. “I don’t think they can take it, though,” he said. “With 80 percent of the population being Shia, it would pretty much be impossible, though they may take Sunni neighborhoods.”

Mideast expert Jonathan Schanzer of the US-based Foundation for Defense of Democracies says ISIS lacks the manpower to hold Baghdad even if it could succeed in storming the capital.

“Strategically for ISIS, invading Baghdad would therefore seem like a mistake,” says Schanzer. But he adds the caveat, “We also don't know what kind of quiet support it enjoys from the disaffected Sunnis -- former Baathists are said to be among ISIS base of support -- who could help the group conquer and hold the seat of power in Iraq.”

The Mideast-based American intelligence official says al-Baghdadi and his inner core of advisers made up of experienced Iraqi jihadists and military veterans -- as well as some Chechens -- are unlikely to make the mistake of trying to mount a full-scale assault on the capital.

He argues the group’s leadership has shown a remarkable grasp of military strategy, astutely withdrawing from towns in rebel-controlled provinces in northern Syria when faced by a backlash from Syrian rebel groups and thus avoiding defeats, negotiating with local Sunni tribes in both Syria and Iraq and entering a pact with former Saddam Hussein-era military officers and Iraqi Baath party members to unleash an audacious Sunni insurgency in Iraq.

Most ISIS military operations have focused on isolating the capital by securing important land routes around it or consolidating their hold on Sunni towns already captured, and by overrunning pockets of resistance in the majority-Sunni zones of western, south-western and northern Iraq bordering Syria, Jordan and Saudi Arabia.

Another priority target has been refineries and oil wells. Already in eastern Syria ISIS has been smuggling and selling oil from wells captured in the uprising against Bashar al-Assad. It’s a lucrative trade that has helped swell the jihadist group’s coffers and transform it into the world’s wealthiest terrorist organization. Taking a chunk of Iraq’s oil production could make it much richer still.

The insurgents are continuing an intense fight at Iraq’s Baiji oil refinery, the country’s largest, despite Iraqi government claims that its forces have asserted full control over the facility.

Meanwhile, a jihadist bombing campaign in Baghdad appears to have started. Two car bombs hit Baghdad’s suburbs during the week, the latest killing 19 and wounding more than 40. Infuriated Shia vowed revenge.

Al-Baghdadi, who appears to be the master strategist, was trained by the late Abu Mousab al-Zarqawi, a Jordanian militant who also defied al-Qaeda’s top leadership. Al-Baghdadi has been following his mentor’s vicious playbook, including beheadings and suicide bombings as well as targeting non-Sunnis or Sunnis opposed to his brand of jihad. Al-Zarqawi believed in the importance of purging apostates – something his follower clearly endorses. The brutality appears to have the terrifying spin-off: inspiring and attracting recruits eager to join in a “successful” jihad, and especially one that has them fighting Shia, whom they consider heretics.

ISIS says it killed at least 1,700 people after seizing the city of Mosul two weeks ago. Refugees from the city told The Daily Beast they had heard that 300 Shia Muslim and Christian inmates of Mosul prison had been executed. And on Friday Human Rights Watch said ISIS had appeared to have massacred Iraqi soldiers – possibly as many as 200 of them -- who had surrendered.

As ISIS no doubt had hoped, its jihadist violence is already triggering a Shia backlash in Baghdad, with reports of dozens of abductions and killings of Sunnis in the capital by vengeful Shia groups. The vendettas are likely to keep Sunnis loyal to the insurgency, if for no other reason than their need for protection.