Mayor Marion Barry stood on the steps of the District Building this week and had his picture taken with Mickey Mouse. Only a mayor brimming with confidence would risk letting that photograph get into the files of his city's newspapers and television stations.

The mouse, visiting the District on a promotional tour, seemed right at home in a political theme park where Tomorrowland, Fantasyland, Frontierland and Adventureland are all rolled up in one: Barryland.

With little more than a year left in his second term, Barry appears to be calling most of the shots and dominating the political landscape here, just the way Uncle Walt used to handle Mickey and his pals in Disneyland.

But all is not necessarily as it seems in Barryland.

For months, Barry has been called invincible by the press and District Building observers anticipating his run for a third term. More recently, however, Barry has appeared somewhat less formidable as he was buffaloed by Congress into supporting construction of a new prison in the District and virtually washed his hands of any responsibility for housing many of the city's homeless.

While no one has stepped forward yet to challenge the mayor, the notion of someone taking on Barry now seems a little less far-fetched. And there is a restiveness of sorts in the office of council Chairman David Clarke that may signal a challenge to the power the mayor wields.

Historically (if 10 years can be said to be history), the office of the City Council chairman has not been the potent counterweight to the mayor's authority that some envisioned it would be. Sterling Tucker, the District's first elected council chairman, found this out when he ran unsuccessfully for mayor in 1978.

Tucker's successor as chairman, Arrington L. Dixon, discovered the chairmanship to be something of a velvet-lined coffin. Dixon's efforts to carve out turf in opposition to Barry cost him support and paved the way for a challenge by Clarke in 1982.

Without coming right out and saying it, Clarke has signaled his discomfort with Barry's increasingly headstrong conduct in office and does little to discourage speculation that he harbors mayoral ambitions of his own. When he is asked by reporters whether he would enter the race for mayor next year, Clarke has declined to rule out that possibility.

Other names have been bandied about by political observers and reporters as potential candidates, mostly the "usual suspects" who ran last time and are reluctant to incur the cost of another bid.

Clarke, not previously bitten by the mayoral bug, may not be so shy. Apart from his coy conversation about making the run, there is other evidence that the chairman is positioning himself for a challenge.

His postures in the council and out in the city suggest that Clarke increasingly sees himself as playing that previously unfulfilled role of counterweight to the mayor.

The council under Clarke has overridden three consecutive vetoes by Barry, including key legislation on interstate banking. In addition, the council has become a more aggressive participant in the budget process, demanding actual expenditure figures of the previous fiscal year to compare with proposed spending for the next.

This week the council, in approving a measure that could block Barry's efforts to nullify a police contract he thinks is too generous, issued a clear statement that it intends to fight Barry on labor issues.

In these contrary council actions, Clarke has not always played a very visible role. Apparently he sees himself as a behind-the-scenes organizer, not a high-profile point man. But as he gets around the city more and more in recent months, Clarke appears to be reminding the electorate that he is a leader.

For example, Clarke spent the last few weeks championing the cause of tenants and the homeless as he campaigned for the rent control referendum and reminded city residents of the District's responsibility to provide homeless shelters.

In the rent control referendum campaign, Clarke revived a minority coalition of six council members who had lost the legislative fight against loosening rent controls last spring, in a successful effort to counter the Barry-led forces opposed to the referendum.

The perception of Clarke opposing the mayor on rent control, interstate banking, the recent no-fault insurance bill and the police contract lends credence to the notion that the council chairman is seeking his own high ground, whether or not he uses it to challenge Barry for mayor.