Faced with a packed agenda and little voter pressure for overhauling the tax code, the House Ways and Means Committee has put off writing a tax overhaul bill until the end of September at the earliest.

In another sign that tax revision is facing tough competition against other legislative priorities, House Minority Leader Robert Michel H. (R-Ill.) yesterday said voters care more for reducing budget and trade deficits than they do for overhauling the internal revenue code.

"There's much more concern about those issues than tax reform, Michel said. "There's no way around it."

His remarks echoed those of House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), who said Wednesday that there is little public support for President Reagan's plan to reduce tax rates and curb numerous deductions and credits. House members streaming back from their congressional districts from the August recess have confirmed that assessment in recent days.

"Almost without exception, the fellows returning from their trips home report that the single emerging issue of greatest public concern is the trade issue," House Majority Leader James C. Wright Jr. (D-Tex.) said yesterday. "The only people who mention a tax reform package are those who have heard of its provisions and are concerned negatively about the impact it would have on them."

Asked whether House members want to act on trade legislation before debating a tax bill, Wright said, "I have been hearing that from my colleagues all day long and yesterday, that the thing they'd like for the House to do would be take a strong decisive stand on an imaginative approach to the trade issue."

Ways and Means Committee members are heading to Virginia hunt country Saturday to try over the weekend to agree on an alternative to the Reagan proposal, but their official work will not start until the week of Sept. 23 at the earliest, committee aides said yesterday. Observers suggested that timetable could easily slip another week.

A tentative schedule had called for Ways and Means Committee members to start writing the massive tax overhaul bill on Sept. 17, and committee Chairman Dan Rostenkowski (D-Ill.) said earlier this year that he wanted to begin work as soon as possible after Labor Day.

Instead, the committee will hold a symbolically important hearing on Sept. 17 on a bill that would impose a surcharge on imports from countries that do not open their markets to American goods. It is sponsored by Rostenkowski, Rep. Richard A. Gephardt (D-Mo.) and Sen. Lloyd Bentsen (D-Tex.). The Ways and Means Committee has jurisdiction over both tax and trade issues.

The delay itself is of relatively short duration. But it makes it less likely that the House can meet the Oct. 15 deadline for completion of a tax bill that Senate Finance Committee Chairman Bob Packwood (R-Ore.) has said he needs if the Senate is to produce tax legislation this year.

Gephardt, who is closely involved with both issues, said he believed the House could approve tax overhaul legislation and a trade bill before the end of the year, and that tax revision will come first.

"I think the members believe both issues are important. There is no reason we can't finish that tax bill in a timely manner and go ahead on the trade issue. The fact of the matter is, you can't do both at once," Gephardt said.

Congressional sentiment is clearly more attuned to trade, however. At a meeting of about 50 leadership Democrats yesterday, Wright asked for a show of hands on issues of concern in their congressional districts. There were many more hands for trade than for taxes.

Ways and Means Committee aides said it is unlikely that the panel will take up a trade bill before it writes tax legislation, because very little substantive work has been done on the trade proposals pending before the committee. However, several other pieces of legislation must be completed this fall.

The statute authorizing the "Superfund" tax to clean up toxic waste dumps expires Sept. 30, and a legislative extension is pending in Congress.

Rostenkowski also will have to shepherd the committee's budget reconciliation resolution on the House floor and move a public works bill, which has a tax component, through his committee in the next few weeks.

Nor has Rostenkowski made several important procedural decisions about pushing the tax legislation through his committee.

Among them are how members will be allowed to propose amendments in a way that will keep tax breaks from creeping back into the measure, raising the federal deficit. Neither has Rostenkowski decided whether the Reagan plan or a hybrid Democratic version will be used as the basis for bill-writing, aides said.

"I would not be surprised to see us [the full House] here until the week before Christmas," Rep. Bill Archer (R-Tex.), a member of the Ways and Means Committee, said.