The White House pointed with pride yesterday to public opinion surveys by Republican pollster Richard B. Wirthlin that show overwhelming approval for the nationally televised speech President Reagan gave last Tuesday in behalf of his tax-overhaul plan.

White House spokesman Larry Speakes said 71 percent of Americans who had heard about the speech said they approved of it and 26 percent disapproved. This favorable rating was exceeded only by the 78 percent approval rating given Reagan's speech to a joint session of Congress on Feb. 18, 1981, Speakes said.

Reagan's overall approval rating was 65 percent, a 4 percentage-point increase from a poll taken last month. Speakes said Wirthlin's surveys gave Reagan a 63 percent approval rating for his overall handling of the economy and a 52 percent approval rating for his management of the budget.

A Newsweek poll yesterday also showed approval for the president's tax plan, but some respondents pointed to potential difficulties for the proposal.

According to the poll, 60 percent of the respondents said they consider the current tax system unfair, and two-thirds of those with an opinion on the subject favored Reagan's plan. However, a majority opposed removing the federal deduction for state and local income taxes, a key feature of Reagan's plan, and opposed taxing "some portion of fringe benefits like health insurance and pension benefits."