In June, Senate Armed Services Committee members approved a $625 billion budget for the Department of Defense (DOD) for fiscal year 2014.
On Wednesday, McCain vowed to raise the issue on the Senate floor once the committee's FY' 14 budget plan is brought to a vote later this year.
Shifting control of armed drone operations, according to McCain. "would be a nice, first measure to assure the American people that there is sufficient oversight of who we are going to kill and not kill."
President Obama announced plans to transition control of the controversial counterterrorism tactic to the Pentagon during a major national security speech in May.
Under the White House's plan, the CIA will continue to supply targeting and other intelligence on possible targets, but operational control over the actual drone strikes would fall to the military.
Currently, the Pentagon and CIA coordinate and execute their own independent armed drone operations in various hot spots across the globe.
That shift was part of an overall effort by the White House to update U.S. counter terrorism strategy from the days directly after the 9/11 attacks.
That overall update will rein in some of the expansive powers handed to the Pentagon and intelligence community to wage war against al Qaeda and its affiliates.
“Unless we discipline our thinking and our actions, we may be drawn into more wars we don’t need to fight, or continue to grant presidents unbound powers more suited for traditional armed conflicts between nation states,” Obama said at the time.
The idea has already generated support from a number of senior Senators.
Handing U.S. military leaders sole control over parts of the program is a major step away from the administration's "status quo" in its aggressive use of armed drone strikes, Sen. Jay Rockefeller (D-W.Va.) told The Hill in June.
The new counter terrorism strategy laid out by Obama in May "sort of shifts things toward DOD, and I think that is a good thing," Rockefeller, the No. 2 Democrat on the Senate intelligence panel, said at the time.
But since Obama's speech in May, efforts to shift control of armed drone operations to DOD have stalled at the Pentagon and in Langley.
Despite the administration's fervor, U.S. military and intelligence leaders "are satisfied with the status quo," according to McCain, who noted the only way to break that impasse is to use the FY' 14 Pentagon budget as leverage.