On July 10, the D.C. Council took a final vote on the controversial legislation mandating a “living wage” for certain large retailers, sending the bill widely seen to be targeting Wal-Mart to Mayor Vincent C. Gray (D) for his signature or veto.

Three weeks later, the bill still hasn’t arrived on Gray’s desk, and the wait has prompted some jawboning between top city officials.

Gray, asked about the bill Wednesday on his monthly NewsChannel 8 appearance, reiterated he was undecided before gently chiding Council Chairman Phil Mendelson (D) for still not having transmitted the bill.

“Normally it would be transmitted sooner, but I think we understand what he’s doing,” said Gray, a former council chairman. “I suspect he’s concerned about the timetable here and making sure his members are available.”

Here’s what he’s talking about: Once Gray receives the bill, he has 10 days to decide on a veto. If he does in fact veto it, the council then has 30 days to schedule an override vote, which requires the assent of nine of 13 members to succeed. The issue is that the council is now on recess and members have dispersed or will soon be dispersing to various vacation destinations. (One of them, Ward 1 Democrat Jim Graham, is in South America.)

If the bill landed on Gray’s desk Wednesday, the council could be in the position of having to vote on an override before Labor Day, with who knows how many members still out of town. A popular John A. Wilson Building conspiracy theory has Mendelson holding the bill because Graham, like Mendelson, is a supporter of the living wage bill, and they can’t afford to have him absent for the override vote.

Occam’s Razor suggests, rather than a conspiracy, that council members would prefer not to disrupt their vacation plans and, all things other being equal, would rather just delay the override vote till the council’s next scheduled meeting on Sept. 17.

By that logic, you can expect the bill to be transmitted no earlier than Monday, Aug. 19 — a date that guarantees the override window will not close before the next regular council meeting.

Reached Wednesday, Mendelson did not dispute that logic, but he also said the debate is “abstract” in that the bill hasn’t even reached his desk for his own signature; it’s still being reviewed by council lawyers and clerks.

Mendelson was also surprised that Gray would suggest the bill was overdue: “In my last conversation with him he did not convey any annoyance.”

If Gray opted to sign the bill, Mendelson noted, it would make little difference whether he did it now or in a month, given that Congress will be in recess from Aug. 5 to Sept. 6, during which time the 30-day congressional review clock would not run. And if Gray opted to veto the bill, he said, it’s not to either side’s advantage to have a mid-recess override vote

“I can tell you, there are members on both sides of the issue who are out of town,” Mendelson said. “If anyone thinks there is an effort at trying to game the vote, that’s not correct.”

He added: “It’s only fair to members that, regardless of what side they’re on, they have the ability to attend if there is an override meeting.”

The suspense notwithstanding, it’s not at all clear anyone gains or loses politically if the bill is dealt with today or a month from now — especially since, according to a recent informal survey of council members and staff, there is little sense that any of the five members opposing the bill are going to change their minds, creating the ninth vote for an override.

The best reason mayoral spokesman Pedro Ribeiro could come up with for a swifter transmittal is this: “It sets a precedent: Should the council hold legislation ad infinitum? What’s to say they couldn’t hold legislation for six month or eight months? … Some kind of standard has to be set.”

Mendelson, who has served on the council since 1999, said the current delay is well within historical standards: “If you look at the history of transmittals, they run the gamut.” One recent bill, he said, spent three months under post-vote review before being sent to Gray.