Maliki may find President Barack Obama and the Pentagon somewhat preoccupied with the Syrian conflict and the question of whether to strike at the regime of Syrian President Bashar Assad, which Maliki supports to some degree.
This could influence how his hosts respond to his desire for more U.S. weapons. But the prospect of deals worth $2.7 billion or more to American defense contractors hustling for export contracts amid cutbacks in U.S. military spending may prove to be irresistible.
Baghdad is already negotiating with Washington and BAE Systems to buy 200 Bradley Fighting Vehicles over the next year or so, BAE officials disclosed recently.
If that comes off, it will allow BAE to keep operating its Bradley assembly line at York, Pa. Another expected Bradley deal with Saudi Arabia would keep it running through 2015.
The U.S. weekly Defense News reports the Iraqi deal is expected to be concluded in 2014 and could involve newly upgraded M2A2 ODS -- Operation Desert Storm -- models.
The Iraqi army currently has 1,000 tracked M113 armored personnel carriers built by BAE.
The U.S. Department of Defense notified Congress in early August of possible new sales to Iraq of air-defense and communications systems worth $2.7 billion.
That raised the total value of proposed U.S. arms deals to Baghdad in recent weeks to around $5 billion.
The biggest of the new proposed sales involves 681 Stinger surface-to-air missiles built by Raytheon Missile Systems and 40 truck-mounted launchers, along with three Raytheon Hawk MIM-23 air-defense batteries with 216 missiles, worth $2.4 billion.
The Stingers can also be fired from Bradley AFVs, and there's an air-launched version for the Apache gunship.
Iraq is buying 36 Lockheed Martin F-16IQ fighter jets, with deliveries of the first 18 under a $4.3 billion deal in December 2011 due to start this year.
The Block-52 jets will be the first combat aircraft for Iraq's post-Saddam Hussein air force.
It's highly unlikely the air force, which is said to be seeking a final inventory of 96 F-16s, will have an operational combat capability until 2015.
That makes acquiring ground-based air-defense systems like the Hawk and the Stinger all the more important.
Maliki is likely to encounter some opposition in Washington to being supplied with the Apache attack helicopters because of concerns the increasingly autocratic Iraqi leader might use then against his own people.
The minority Sunnis, who claim they're being discriminated against by Maliki's Shiite, Tehran-leaning coalition and have clashed with Iraq's largely Shiite security forces, are possible targets.
So is the independence-minded Kurdish minority which is defying Baghdad by producing and exporting its own oil in its semiautonomous northern enclave.
They don't want the Americans to sell Maliki the F-16s because they fear the jets will be used against them. Maliki declared Aug. 14 he will continue his harsh crackdown on "terrorists."
The House Foreign Affairs Committee and the Senate Foreign Relations Committee have refused so far to allow sales of Apaches, which are ideal for counter-insurgency operations, to Maliki.
With his regime widely suspected of allowing Iranian aircraft to overfly Iraq to deliver weapons to the beleaguered Assad regime despite U.S. protests, the Iraqi leader may once again be refused.
But it's clear Maliki needs weapons systems like the Apache to counter al-Qaida networks currently engaged in a murderous bombing campaign in Baghdad and other cities -- and which have recently begun attacking oil centers in Shiite-dominated southern Iraq that are operated by Western oil companies.
Such sales could go a long way toward maintaining U.S. influence in Baghdad, where it has been flagging since U.S. forces withdrew in December 2011 -- as witnessed by a $4.3 billion arms deal with Russia in October 2012.
That involves 40 Mil Mi-28NE all-weather attack helicopters worth $2 billion and 42 Pantsir S-1 short-to-medium range SAM systems worth $2.3 billion.
If that lineup looks a lot like the Apaches and Hawk-Stinger package that Maliki's hustling for in Washington, it could suggest he's trying to bargain with the U.S.
Moscow, a key arms supplier to the Saddam Hussein regime, would love to trump Obama right now.