Democrats from the House Budget Committee began a week-long, cross-country assault on President Reagan's budget priorities here today in one of the opening moves in an election-year battle over spending, taxes and the federal deficit.

At the first of five scheduled hearings around the country, Reagan's fiscal 1987 budget was denounced by a parade of witnesses, including Chicago's Democratic mayor, Harold Washington, who accused the president of having "declared war" on his and other U.S. cities.

The committee hearings are part of a Democratic strategy to focus attention on the Reagan budget and tie Republicans to the administration's call for eliminating or drastically reducing a number of politically popular domestic programs.

But it was clear from the outset that House Republicans -- none of whom attended today's hearing -- do not plan to cooperate in this effort. The GOP attitude was summed up by House Minority Leader Robert H. Michel (R-Ill.), who called the committee's week of field hearings "a dog and pony show" having little to do with the federal budget.

"The fact that Republicans are not participating makes it kind of a charade," Michel told a news conference in nearby Peoria, Ill.

Budget Committee Chairman William H. Gray III (D-Pa.) was prepared for the Republican boycott, which he said was "unfortunate" but would not affect the hearings.

"I don't blame them," Gray said. "I'd run and hide from it the Reagan budget , too."

Gray said that despite last week's federal court ruling that struck down a key provision of the new Gramm-Rudman-Hollings balanced-budget law, his committee would produce a budget resolution meeting the law's $144 billion deficit target for fiscal 1987. "At some point, when the Republicans can't run any further, they will have to sit down and deal with the reality," he said.

Questioning witnesses at the hearing, Gray suggested that he favored a freeze or cuts of up to 20 percent in many programs slated for elimination in the Reagan budget to keep those programs alive while reducing the deficit. "I always say something is better than nothing," Mayor Manny Hoffman of suburban Homewood replied when asked if he would support such an approach.

Hoffman said his constituents wanted the same level of services without a tax increase, and he agreed with Gray that the federal government faced the same demands from voters.

"It's a good trick if you can do it," he said.

Other committee members focused on reducing the deficit by raising revenues. Asked by Rep. Marty Russo (D-Ill.) if the business community would support a cut in defense spending and a tax increase, Leo Melamed, chairman of the Chicago Mercantile Exchange, said, "There clearly have to be some shifts in budget priorities and some additional revenues. We don't deny that."

About 100 people attended the hearing, including competing groups of demonstrators. One group held signs saying "Reagan Mandate -- No Tax Increase" while the other demanded "No More Cuts in Social Programs."

Only three Democratic members of the Budget Committee -- Gray, Russo and Patrick Williams (Mont.) -- attended the hearing. They were joined by five other House Democrats from the Chicago area.

Mayor Washington told the committee that federal aid to Chicago was cut by $155 million this year and will shrink by another $268 million in 1987 under the Reagan budget, which he likened to a "war on the city of Chicago."

Marian Wright Edelman, president of the Children's Defense Fund, chided Reagan for voicing "profamily" rhetoric in his State of the Union address while proposing a budget that she said would cut more than $6 billion from programs that aid children.

Other witnesses said the proposed Reagan budget cuts would cripple employment, health, housing, transportation and other programs in communities across Illinois. Throughout the hearing, Gray sought to contrast Reagan's upbeat State of the Union message with the specifics of the budget. "You paint an entirely different picture than the one painted for Congress and the American people last week," he told Edelman after she had recited statistics on the mounting problems of children.

Gray did not deny the underlying political purpose of the field hearings, which are scheduled to continue in Lowell, Mass.; Tallahassee, Fla.; Dallas and San Francisco. "We are a political body," he said.