The overtime battle between the two largest federal employee labor organizations finally ends Tuesday, with the close of a month-long runoff union election for transportation security officers.

With 44,000 officers in the bargaining unit, this election has been closely watched inside and outside of government. The fight to represent the officers who screen people and baggage at the nation’s airports is the largest union organizing effort in the federal government’s history and the largest current labor organizing campaign in the country.

There was a sense of excitement that an exclusive bargaining agent would at last be selected as the last day of voting approached — and a clear feeling of relief that this whole process is almost over.

“At this point, everybody just wants this to be done,” said Kathy Phillips, a lead TSO and president of the American Federation of Government Employees local at Dulles International Airport.

Employees are ready, said National Treasury Employees Union President Colleen M. Kelley, to “move forward and bargain for their first contract.”

The Federal Labor Relations Authority will announce the winner Thursday.

AFGE and NTEU have poured lots of money, people and other resources into the campaign, probably more than they ever intended. As big as the victory will be for one, the disappointment for the other will be huge.

Both organizations have worked aggressively, including some negative campaigning, to get out their vote for the runoff. Neither union was thrilled with the turnout last time. It was a particular disappointment to AFGE, which had claimed some 13,000 members among TSOs. And a loss certainly would not help Kelley’s campaign to be reelected president of NTEU.

“Both unions are working really hard to get those who were undecided,” said Eric Rosario, a NTEU shop steward at Reagan National Airport. He cited campaign events at airport hotel restaurants and union barbecues, in addition to the traditional leafleting.

“That’s going to be a big leg up for whomever wins the election,” he said.

Unless the two unions manage to get exactly the same number of votes, this time one will be able to declare victory.

A runoff was necessary because a six-week voting period that ended in April concluded with no clear winner. AFGE got 8,369 votes, while NTEU got 8,095. But because the “no union” option took 3,111 votes, none of the ballot choices had a clear majority of the 19,585 votes cast.

Only AFGE and NTEU are on the runoff ballot.

Despite the additional campaigning, AFGE President John Gage doesn’t expect an increased turnout for the runoff. “I do think it’s going to be a relatively low vote total and probably closer than it should be,” he said.

Kelley wouldn’t guess at the voter turnout, “but we don’t have to wait long,” she said.

The Performance Accountability and Standards System, the pay-for-performance system applied to TSOs, is the highest priority on the hit list for both unions. Employees don’t trust PASS, and the unions have vowed to end it. However, “pay and policies affecting pay” are excluded from bargaining under the rules issued by John Pistole, head of the Transportation Security Administration, when he granted collective bargaining rights to TSOs in February.

The limited collective bargaining rights also exclude any issue that TSA considers security-related, including security procedures and the deployment of security personnel and equipment. Also excluded from bargaining are compensation, testing, job qualifications and discipline standards.

Bargaining is permitted at the national level only. Items available for negotiations include shift bids, transfers and awards.

The two unions and their presidents, now vigorous rivals, have cooperated on many issues affecting the federal workforce. They probably will try to continue that cooperation, even though this campaign turned so nasty that one union took the unusual step of filing a lawsuit against the other.

AFGE asked the D.C. Superior Court to order NTEU to stop spreading what AFGE said were lies. AFGE objected to an NTEU leaflet that claimed AFGE provided “no representation for $3.4 million in dues AFGE receives each year from its TSA members.” The flier also pointed to “AFGE’s $20 million of debt.”

In addition to the suit, AFGE responded with its own flier that said: “NTEU lied about AFGE’s finances. NTEU lied about AFGE’s representation. Do they lie about everything?”

The negative turn surprised William R. Dougan, president of the National Federation of Federal Employees and chairman of the Federal Workers Alliance.

“I hope that we all recognize that we have to be in this fight to protect federal workers together” against attacks from Congress and the media, he said. “I’m hopeful and confident that Colleen and John understand that.”