Budget director David A. Stockman warned today that Congress' political "gridlock" could result in failure to pass a fiscal 1984 spending plan, and Senate Finance Chairman Robert J. Dole (R-Kan.) urged President Reagan to step in.

But the president reaffirmed his opposition to any tax increases for the next two fiscal years, despite warnings Friday from Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) and Budget Committee Chairman Pete V. Domenici (R-N.M.) that the White House must compromise on taxes if it wants to be part of the congressional budget process.

"Governments don't reduce deficits by raising taxes on the people," Reagan said in his weekly radio speech, broadcast from Camp David, Md., in which he discussed his administration's efforts to help small business.

Stockman, referring to the Senate's failure this week to approve a budget resolution, said that the fiscal 1984 budget process "is in a very precarious state."

"We seem to be facing a gridlock in terms of those major elements where movement has to take place, entitlements, domestic spending, defense and on the tax side," he said.

Dole urged Reagan to meet with leading lawmakers on the budget impasse. He said that the president "must play a role in this budget process even though it's a congressional discipline. We can't tolerate the big deficits."

The president's chief economic adviser, Martin S. Feldstein, warned that congressional failure to reduce future-year budget deficits poses a "non-trivial risk" that "we will see the recovery petering out in a year or two years."

Feldstein, Stockman and Dole spoke with reporters after their separate closed-door speeches to the semi-annual meeting of the Business Council, composed of more than 100 of America's top chief executives.

According to a Senate aide in Washington, Domenici returned from a White House meeting Friday "as angry as I've ever seen him." The aide quoted Domenici as saying, "We're going to get a budget resolution, and it's up to them the White House if they're going to come along."

Domenici and Baker reportedly said after their White House meeting that they are seeking an $8 billion increase in revenues for 1984 and between $13 billion and $15 billion in 1985.