It would take the Senate approximately 700 hours of floor time to individually process and vote on hundreds of military officers whose promotions are being blocked by Alabama Republican Sen. Tommy Tuberville, the Congressional Research Service concluded in a memo released on Tuesday.

The number of pending nominations has only increased since the memo was written in late August, from 273 to over 300 today.

Senate Armed Services Chairman Jack Reed, a Rhode Island Democrat, asked the CRS to estimate the amount of time it would take to process each of the nominees individually, instead of taking them up and confirming them as a group by unanimous consent -- "the only way to process multiple nominations quickly," according to the CRS.

The Senate has been unable to confirm the nominees by unanimous consent because Tuberville has said he would object. He has placed a blanket hold on the nominations in protest of the Pentagon's reproductive health policies, and the pending promotions of the military officers continue to pile up, leaving dozens of service members in limbo.

Tuberville has repeatedly responded to criticism of his hold by saying that Senate Majority Leader Chuck Schumer could theoretically bring each nominee to the floor, one-by-one, and confirm them.

While technically true, doing so "would take the Senate approximately 689 hours and 20 minutes of floor consideration, plus two days of session at the start of the process for cloture to mature on all 273 nominations," the Congressional Research Service concluded in its memo.

"This total represents approximately 30 days and 17 hours to process all 273 military nominations, assuming the Senate worked 24 hours a day without break or interruption by other business. Alternatively, based on the above assumptions, if the Senate exclusively processed these nominations during eight-hour session days, it would take approximately 89 days to confirm all 273 nominees," the memo stated.

Democratic senators have also signaled they are not willing to vote on only the most high-profile nominees, because that would send the wrong message to the rank-and-file.

"To vote on 300 non-controversial nominations, with Senator Tuberville demanding maximum time on each, could take us to the end of the year," Virginia Democratic Sen. Tim Kaine, who sits on the Armed Services Committee, told CNN last week.

"The other offer someone said is, why don't you pick some of the top people like the service chiefs and vote on them and then just let Sen. Tuberville punish those down the ranks?" Kaine added. "That is not the way the military operates. Officers say, officers eat last. You don't punish the people down the ranks to advantage people up the ranks."

Republicans have criticized Tuberville's hold, too. House Foreign Affairs Chairman Mike McCaul, a Texas Republican, told CNN's Jake Tapper on Sunday that the senator's hold is "paralyzing" and a "national security problem."

"The idea that one man in the Senate can hold this up for months ... is paralyzing the Department of Defense," McCaul said. "I think that is a national security problem and a national security issue."