After three days and nights of almost solid, bitter politics, the American Federation of Government Employees started to get down to business yesterday. It talked about financing the government's biggest union, and stepping up organizing efforts so that the AFGE doesn't become the government's second biggest union.

Most of the 1,500 delegates and alternates here seemed relatively calm and subdued Thursday after a bitter week of politicking charges and counter-charges. The potential for an ugly aplit was present, since Philadelphia regional vice president Royal Sims came within 1,000 votes - out of more than 216,000 ballots cast - of winning a simple majority victory over incumbent president Kenneth T. Blaylock.

Although the union business now centers on resolutions and money talk, delegates will be doing it while suffering from bad political hangovers. Blaylock didn't exactly bury the hatchet in the traditional victory speech of a winning politician. He did ask the union to close ranks. But he made it clear that some of the national vice presidents who opposed him will either shape up, or spend the next two years straddling a giant political razor balde.

The official count from Wednesday night's election gave Blaylock 109,414 votes to 107,052 for Sims. A shift of just over 1,000 to Sims - one or two small union locals - would have given him the simple majority to win.

Oldtimers say it is the closest presidential race in history. And it reflects membership bitterness with Blaylock for backing President Carter's civil service reform plan. It was also the only way these union members could strike out at Jimmy Carter.

National secretary-treasurer Nicholas Nolan led the voting, drawing 118,897 votes. But he faced an unusually strong challenge from little-known William Nussbaum, a social security worker from New Jersey. After campaigning only six weeks, he got nearly 96,000 votes. Insiders believe Nolan would have won bigger if he had not endorsed and campaigned for Blaylock. Most other national officers remained neutral, or opposed Blaylock under cover.

Louise Smothers of Washington was reelected women's coordinator for the union, a controversial job whose very existence and status caused a division between delegates. While reelecting Smothers nearly 2-to-1 over challenger Esther Johnson, a former AFGE afficial, the convention voted down a resolution to give the coordinator a seat on the National Executive Council. It is now an all-male preserve made up of vice presidents who are elected regionally.

Blaylock said he would support the convention's strong directive not to go along with the Carter civil service reforms. But he said he will try to get members to allow him to work for passage of a House version of the bill. That legislation, which is expected to come to the House today, goes well beyond the "reforms" Carter has proposed. While giving management a freer hand to deal with workers, it also gives unions more collective bargaining clout, provides downgrading protection for workers, and would allow employes to take active roles in partisan politics.

The Chicago Tribune yesterday had its lead editorial on civil service reform. The Tribune said it favored reforms as outlined by Carter, and the U.S. Chamber of Commerce, but opposes the House version. It said the House bill would politicize the government, and turn the reins of power in the bureaucracy over to the unions. The editorial was xeroxed by the thousands and distributed to delegates here. Except for that editorial, the Chicago papers have generally ignored the actions of the convention here.

In a press conference, Blaylock made it clear he is bitter and unhappy with some of his national vice presidents. He said some of them had failed to tell members the truth about civil service reform, or had failed to tell them anything. Blaylock refused to identify the national officers but he said they know who they are and will know how strongly he feels about their alleged failures shortly. He also blamed Carter administration salesmen, who have lobbied businesses, the media and civic groups on civil service reform for using dangerous trigger words and slogans to sell it.

Among the pitches made by administration aides, Blaylock said, was the crowd-pleaser that civil service reform would make it easier to fire bureaucrats. That sort of talk might do well with some segments of the public, misinformed by a sensation-seeking press, Blaylock said. But it doesn't sit well with his members.

Asked if he would take a more active role in communicating with rank and file members, Blaylock said he would "go over the heads" of national vice presidents who he believes aren't doing their jobs.

The union rejected a proposal to raise dues 65 cents from $3.40 per member per month to $4.05. Insiders believe the proposal will come up again and the convention will approve some sort of increase. Federal employe union dues are incredibly low by private industry standards primarily because unions do not have strike funds and because many of the costs of negotiating and other sevices are partially borne by the government.