CHARTER OR NO CHARTER, Washington's local leaders still must go hat-in-hand to Congress each year for the city's allowance and approval of ways it can be spent. That's something most of us would like to see fixed, of course, but in the meantime there are some differences for the better in the manner in which the budget is considered these days.

First, the elected city government has greater powers to tax. It also has a healthy political responsibility to hear down on spending. No longer can top city officials merely shrug and point toward Capitol Hill when constituents complain about curtailed city services. Indeed, except for a few naughty fiscal orders and cuts here and there, Congress hasn't been fiddling all that much with the city's spending proposals lately.

But there are constructive differences of opinion inside city hall over how money should be raised and spent. Just this week, for example, the city council has been shaving and reshaping supplemental budget requests and amendments that Mayor Washington wants to sent to the White House and Congress.

In this latest budget round, the city council's proposed cuts in Mayor Washington's spending requests would allow for some tax relief as well as certain appropriations for specific city services. Half of the council's total budget reduction would come from a $5-million cut in the amount the mayor has proposal in this instance for the Department of Human Resources for welfare payments.

It is true that cutting welfare payments is an old congressional antic. But what the city council is doing is different. It is urging DHR to make up this amount not by cutting payments, but by purging its rolls of ineligible recipients. As we noted in this space the other day, DHR's error rate on this score is horribly high; mistakes are costing the city an estimated $16 million annually in improper payments. Given this record, there's no great reason to believe that the council action will produce big results - but anything's worth a try at this point.

In addition, the council proposes allowances for either a 9-cent reduction in the real-estate tax or a homeowner deduction of $6,000 from each home-property assessment before calculating taxes at the present rate. As it now looks, the twice-weekly trash collections would continue, street and alley cleanings would suffer and those street lights wouldn't start going out just yet.

Also, thanks to provisions in the charter, Mayor Washington is subject to a fixed deadline for reacting to the council's moves once a formal decision is transmitted to him. So if all goes well, the mayor and city council should be able to reach agreement on a thoughtful attempt to balance cuts in services with possible - and welcome - savings in constituents' tax bills.