(CNN) Secrecy is the linchpin of a stealth aircraft's ability to carry out strikes deep within enemy territory, but when it comes to the tax dollars that are going to be spent on the U.S. Air Force's new B-21 bomber, some members of Congress say it is time pull the curtain back.

The Air Force said it has no plans to publicly disclose the cost estimate for the aircraft touted as the "backbone" of the U.S.'s future strike and deterrence capabilities, arguing it would reveal too much information to potential adversaries and compromise a classified program.

That's infuriated some lawmakers, including Sen. John McCain, who argue that the public deserves to see the price tag because so many defense projects have blown their budgets due to waste and fraud.

Officials have been tight-lipped as to the specific capability expectations for the B-21, but indications are that it will be stealthy, able to carry conventional and nuclear weapons, and could possibly operate with or without a pilot.

"Releasing that [data], releasing other things that may be more insightful to our adversaries, I don't think helps the taxpayer and I don't think it helps -- certainly -- the warfighter," Randall Walden, program executive officer of the Air Force's Rapid Capabilities Office, said at an event earlier this month hosted by the Mitchell Institute for Aerospace Studies.

"All we're doing is putting in that risk and we're showing our hand of what we believe this nation and the states' workers can deliver this particular weapon system for," added Walden, whose office is responsible for procuring the bomber and other classified weapons systems.

Photos: In the U.S. Air Force fleet B-52 Stratofortress – The first versions of this long-range heavy bomber flew in 1954. A total of 744 were built, the last of those in 1962. The Air Force maintains 58 B-52s in the active force and 18 in the Reserve. A single B-52 can carry 70,000 pounds of mixed munitions, including bombs, missiles and mines. The eight-engine jets have a range of 8,800 miles. Hide Caption 1 of 24 Photos: In the U.S. Air Force fleet C-130 Hercules transport – A C-130J Super Hercules from the 37th Airlift Squadron flies over Normandy, France, June 3, 2015. First delivered to the Air Force in 1956, the C-130 remains one of the service's most important airlift platforms. More than 140 are still in active units, with more than 180 in the National Guard and a hundred more in the Reserve. The C-130 is powered by four turboprop engines. Hide Caption 2 of 24 Photos: In the U.S. Air Force fleet AC-130 gunships – The AC-130H Spectre and the AC-130U Spooky gunships are designed for close air support, air interdiction and force protection. Armaments on the Spectre include 40mm and 105mm cannons. The Spooky adds a 25mm Gatling gun. Hide Caption 3 of 24 Photos: In the U.S. Air Force fleet F-22 Raptor – The twin-engine F-22 stealth fighter, flown by a single pilot and armed with a 20mm cannon, heat-seeking missiles, radar-guided missiles and radar-guided bombs, can perform both air-to-air and air-to-ground missions. The service has 183 of the Raptors, which went operational in 2005. Hide Caption 4 of 24 Photos: In the U.S. Air Force fleet The single-engine F-35A is the Air Force's eventual replacement for the F-16 and the A-10. The supersonic jets, which will be able to conduct air-to-air and air-to-ground attacks, are just beginning to enter the Air Force fleet. Here, an F-35 Lightning II from the 34th Fighter Squadron at Hill Air Force Base, Utah, flys at Royal Air Force Lakenheath, England, April 15, 2017. Hide Caption 5 of 24 Photos: In the U.S. Air Force fleet B-2 Spirit bomber – The four-engine B-2 heavy bomber has stealth properties that make it hard to detect on radar. Flown by a crew of two, it has an unrefueled range of 6,000 miles and can deliver both conventional and nuclear bombs. Twenty B-2s are in the active inventory. They joined the fleet in 1997. Hide Caption 6 of 24 Photos: In the U.S. Air Force fleet B-1B Lancer bomber – The four-engine jet can fly at 900 mph and carry the largest payload of bombs and missiles in the Air Force inventory. The Air Force has 62 B-1Bs in the fleet. Hide Caption 7 of 24 Photos: In the U.S. Air Force fleet F-15 Eagle – The F-15 Eagle, the Air Force's main air superiority fighter, became operational in 1975. With a crew of one or two, depending on the model, the twin-engine jets are armed with a 20mm cannon along with Sidewinder or AMRAAM missiles. The Air Force lists 249 F-15 Eagles in its inventory. Hide Caption 8 of 24 Photos: In the U.S. Air Force fleet F-15E Strike Eagle – The Strike Eagle is a version of the air superiority fighter adapted to perform ground-strike missions. With a crew of two, the twin-jet can carry and deploy most weapons in the Air Force inventory and operate in any weather. The F-15E was first delivered in 1988. The Air Force lists 219 in its fleet. Hide Caption 9 of 24 Photos: In the U.S. Air Force fleet A-10 Thunderbolt – The A-10 Thunderbolt jets, nicknamed "Warthogs," are specially designed for close air support of ground forces. Key to their armaments is a 30mm Gatling gun. The pilot is protected from ground fire by titanium armor, and the plane's fuel cells are self-sealing in case of puncture. Hide Caption 10 of 24 Photos: In the U.S. Air Force fleet RC-135U – The RC-135U Combat Sent, based at Offutt Air Force Base, Nebraska, provides strategic electronic reconnaissance information to the president, secretary of defense, Department of Defense leaders and theater commanders. Hide Caption 11 of 24 Photos: In the U.S. Air Force fleet An F-15 Eagle takes off from the Andersen Air Force Base, Guam, flight line as two E-3 Sentries are seen in the background. Hide Caption 12 of 24 Photos: In the U.S. Air Force fleet OV-10 Bronco – A 21st Tactical Air Support Squadron OV-10 Bronco aircraft fires white phosphorus rockets to mark a target for an air strike during tactical air control training. Hide Caption 13 of 24 Photos: In the U.S. Air Force fleet A-29 Super Tucano – An A-29 Super Tucano taxis on the flightline during its first arrival, Sept. 26, 2014, at Moody Air Force Base, Georgia. Afghan Air Force pilots trained on the planes that will be used in air-to-ground attack missions in Afghanistan. Hide Caption 14 of 24 Photos: In the U.S. Air Force fleet KC-135 Stratotanker – The four-engine KC-135 joined the Air Force fleet in 1956 as both a tanker and cargo jet. It can carry up to 200,000 pounds of fuel and 83,000 pounds of cargo and passengers in a deck above the refueling system. More than 400 of the KC-135s are flown by active, Air Guard and Reserve units. Hide Caption 15 of 24 Photos: In the U.S. Air Force fleet F-16 Fighting Falcon – The single-engine jet is a mainstay of the Air Force combat fleet. It can perform both air-to-air and air-to-ground missions with its 20mm cannon and ability to carry missiles and bombs on external pods. More than 1,000 F-16s are in the Air Force inventory. Hide Caption 16 of 24 Photos: In the U.S. Air Force fleet C-17 Globemaster transport – The four-engine jet joined the Air Force fleet in 1993 with a primary mission of troop and cargo transport. Each plane can carry up to 102 troops or 170,900 pounds of cargo. The Air Force has 187 C-17s on active duty, 12 in the Air National Guard and 14 in the Reserve. Hide Caption 17 of 24 Photos: In the U.S. Air Force fleet C-5 Galaxy transport – The C-5, with a wingspan of 222 feet, a length of 247 feet and a height of 65 feet, is the largest plane in the Air Force inventory and one of the largest aircraft in the world. The first versions of the four-engine jet joined the force in 1970. The Air Force expects to have 52 versions of the latest model, the C-5M, in the fleet by 2017. Hide Caption 18 of 24 Photos: In the U.S. Air Force fleet CV-22 Osprey – The Osprey is a tiltrotor aircraft that combines vertical takeoff, hover and landing qualities of a helicopter with the normal flight characteristics of a turboprop aircraft, according to the Air Force. It is used to move troops in and out of operations as well as resupply units in the field. The Air Force has 33 Ospreys in inventory. Hide Caption 19 of 24 Photos: In the U.S. Air Force fleet E-3 Sentry AWACS – AWACS stands for airborne warning and control system. This four-engine jet, based on a Boeing 707 platform, monitors and manages battle space with its huge rotating radar dome. The planes have a flight crew of four supporting 13 to 19 specialists and controllers giving direction to units around the battle space. The Air Force has 32 E-3s in inventory. Hide Caption 20 of 24 Photos: In the U.S. Air Force fleet KC-10 Extender – Based on the DC-10 passenger jet, the triple-engine KC-10 is a gas station in the sky with the ability to carry 75 people and 170,000 pounds of cargo. In its six tanks, the KC-10 can carry up to 356,000 pounds of fuel and dispense it while airborne. The Air Force has 59 KC-10s on active duty. Hide Caption 21 of 24 Photos: In the U.S. Air Force fleet T-38 Talon – The twin-engine jet trainer, used by the Air Force to prepare pilots for the F-15E Strike Eagle, F-15C Eagle, F-16 Fighting Falcon, B-1B Lancer, A-10 Thunderbolt and F-22 Raptor, first flew in 1959. Almost 550 are in the active force. Hide Caption 22 of 24 Photos: In the U.S. Air Force fleet U-2 – The single-engine, single-pilot U-2 is used for high-altitude reconnaissance and surveillance. Flying at altitudes around 70,000 feet, pilots must wear pressure suits like those worn by astronauts. The first U-2 was flown in 1955. The planes were used on missions over the Soviet Union during the Cold War, flying too high to be reached by any adversary. The Air Force has 33 U-2s in its active inventory. Hide Caption 23 of 24 Photos: In the U.S. Air Force fleet WC-135 Constant Phoenix – The four-engine WC-135 is used to fly through airspace to detect the residue of nuclear blasts. "The aircraft is equipped with external flow-through devices to collect particulates on filter paper and a compressor system for whole air samples collected in holding spheres," the Air Force says. It has two of these jets in the active force. Hide Caption 24 of 24

But the service has faced pressure from several lawmakers to release the data, including the fees paid to defense contractor Northrup Grumman, which is building the sophisticated, nuclear-capable bomber, so that the taxpayers can see if the program is being properly managed.

"At a time of growing threats and fiscal constraints, American taxpayers want to know if the Pentagon is spending their hard-earned money effectively and efficiently," McCain, one of the program's harshest critics, told CNN. "The Air Force must release the total contract award value of the Long Range Strike Bomber to ensure this program and the people managing it are held accountable."

The Air Force has already released some financial info, but it's not the whole picture, by any means. It was disclosed that the B-21's per-plane cost is expected to come in at roughly $560 million, although that was a preliminary estimate made by the Department of Defense before Northrup Grumman had even won the contract to build the plane. The amount that the government is paying the defense contractor for the new stealth program is secret.

The Pentagon also made public an artist's conception of the aircraft, which some lawmakers argue would be more useful to a foreign intelligence agency than the overall contract cost.

Recent programs to upgrade stealth air capabilities, including the F-35 Joint Strike Fighter, have been plagued by schedule delays, technology glitches and cost overruns.

But the flaws of some past defense programs have not swayed most of McCain's colleagues to join his call for more transparency when it comes to the B-21's price tag.

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The Senate House Armed Services Committee recently voted 19-7 to limit revealing the B-21 program's total cost estimate to only members of congressional defense committees, rather than full public disclosure, during a closed-door session to discuss the details of its annual defense policy bill.

Voting in favor of keeping the number a secret from the public were Republicans James Inhofe, Jeff Sessions, Roger Wicker, Deb Fischer, Mike Rounds, Thom Tillis, and Mike Lee. They were joined Democrats Jack Reed, Bill Nelson, Richard Blumenthal, Claire McCaskill, Joe Manchin, Jeanne Shaheen, Kirsten Gillibrand, Joe Donnelly, Mazie Hirono, Tim Kaine and Martin Heinrich.

Republican Senators Kelly Ayotte, Tom Cotton, Joni Ernst, Dan Sullivan, Lindsay Graham and Ted Cruz joined McCain in opposition to the secrecy.

"The Air Force has repeatedly said, citing National Security concerns, that it will not declassify the amount of Northrop Grumman's bid for the project because, as has been demonstrated in the past, doing so would allow our adversaries to use the costs associated with the program to glean information about the B-21 such as what equipment is going on it, its weight, how high it can fly, how fast it can go and how far it can travel," said a spokesman for Sen. Bill Nelson.

"Sen. McCain introduced a provision during the Armed Services Committee mark-up of the National Defense Authorization Act that would have, in effect, killed the B-21 program unless the Air Force publicly disclosed how much Northrop bid to win the project," the aide added.

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Northrop Grumman, the developer of the Air Force's current bomber, the B-2, beat out a partnership between aeronautic juggernauts Boeing and Lockheed Martin last year for the right to build the next generation of long-range aircraft.

The Air Force said it plans to start testing the plane sometime in the mid-2020s and hope to replace the B-1 bomber when they retire sometime in the 2040s.