City Council Member Arrington Dixon's campaign kickoff last week had most of the usual political paraphernalia. There were buttons, balloons, T-shirts, posters, signs and even politicians and would-be politicians going around kissing children. That's the part 7-year-old Drew Dixon, the daughter of the candidate for council chairman, apparently didn't like.

Drew was standing on the steep steps leading up to the Federick Douglass home on Cedar Hill, where her father was soon to make his announcement, when she told her sister and a playmate about some of usually unknown trials and tribulations of being a political child.

"Everybody knows our daddy and everybody knows us," Drew complained. "So everybody's kissing us and I'm getting sick of it."

The expectation now is that as much as $1 million could be spent in this fall's city elections. Four candidates alone - three contenders for mayor and one for City Council chairman - are each budgeting in the neighborhood of $200,000. That has led some campaign finaciers to wonder if there will be enough money to go around.

If there is not, it will mean that those who planned to give a little money to each of the candidates may have to change their plans. It may not be possible, in light of the large demand for campaign financing, to put a little money on all the political horses, thereby making sure that whoever loses, you still win.

"We can't get a million dollars," said one fundraiser who is anteing up the cash for one mayoral candidate and one Council chairman hopeful. "People will just have to make choices. The money just isn't there. It's a problem."

R. Robert Linowes, president of the Metropolitant Washington Board of Trade, is somewhat more optimistic.

"If it's important enough, it can be raised, and I think it is important enough. It's very ambitious, but there is the potential," Linowes said.

He, too, thinks the days of a dollar in every kitty are over, but for more than one reason. "There's going to be less of that than occurred previously because the business community is beginning to realize it's going to have to take positions," he said.

All of this is likely to pose a real challenge to businessmen, professionals and laborites, who make up the main source of campaign finances in this town and have just been introduced to the idea of giving to local campaigns. In the past, most city money has gone to federal campaigns because the real power in District affairs rested in the White House and on Capitol Hill.

"When you put in the perspective of a million dollars, that's an awful lot of money," said Board of Trade Executive Vice President John R. Tydings. "What it says to me is that there's going to be a real need for a broadening of sources from the past years."

Mayrol candidate Marion Barry, the former director of Pride, Inc., is hard at work with his campaign staff trying to shed the image of a shouting black militant from the days of yore. But that effort has not stopped the Barry organization from passing up a good joke.

A couple of weeks ago, campaign manager Ivanhoe Donaldson pointed to a picture of Stokeley Carmichael, former chairman of the Student Non-violent Coordinating Committee, on the wall of the campaign office and joked to candidate Barry that perhaps a spot could be found for Carmichael in a Barry administration.

"We ought to tell John Tydings (executive vice president of the Metropolitan Washington Board of Trade) that that's his new budget director," Donaldson said with a smile.