White House chief of staff Donald T. Regan acknowledged yesterday that President Reagan's proposed tax overhaul is running into obstacles and faces some probable changes, but he predicted that the administration would be able to "retain the essence" of the plan and win congressional approval this fall.

The president, despite criticisms of the way the White House is selling the proposal, will continue a series of speeches across the country aimed at igniting public interest, Regan said. He also said Reagan will continue to vary the arguments he uses in these speeches because "we're in danger of boring ourselves if we repeat the same themes."

"The tax message is out there and we've got to keep it out there," Regan said in an interview. "We cannot avoid talking about it, talking about it, talking about it because it's a very complicated subject, not too well understood. People have a fear of changing the tax code because they think it will hurt them."

Regan said the "essence" of the bill includes reducing the number of tax brackets, closing loopholes, imposing a minimum tax and doubling the personal exemptions. He also said that Reagan will stay firm on the proposed 35 percent top rate for indviduals, despite pressures from Republican conservatives to lower it to 30 percent and from some Democrats to raise it to 40 percent.

In the three weeks since Reagan proposed the tax revision as the cornerstone of his "second American revolution," administration officials have been at odds on how to sell the program to Congress and the country.

"We're having a debate between 'fairness' and 'family,' " one official said. "We can't decide how to sell it."

Some officials, such as White House communications director Patrick J. Buchanan, have stressed the "family" part of the equation, emphasizing the proposed doubling of the individual tax exemption -- which will benefit large families. Others, like political adviser Edward J. Rollins, underline the "fairness" aspect of raising corporate taxes and requiring a minimum corporate and individual tax.

One official said "we've left the fairness issue to the Democrats when we've got a plan that could take it away from them." Other officials say that there is no overall strategy for selling the tax program, that instead decisions are being made case by case.

"The speech writers haven't sat down with the policy people," one source said. "We do everything ad hoc. We're relying solely on the communicative skills of the president, and he needs some support on the ground."

As an example of the problem, an official cited conflicting tactics that have been used in pursuit of bipartisan support.

On May 28, when Reagan unveiled his tax plan, he was followed on national television by Rep. Dan Rostenkowski (D-Ill.), influential chairman of the tax-writing House Ways and Means Committee, who praised the president and embraced the goals of the tax revision.

But the president immediately launched a series of trips in which his tax speeches were followed by speeches at Republican fund-raisers attacking the Democrats. Rostenkowski complained, and the White House is now trying to keep Reagan's tax speeches separate from his partisan appearances.

On Thursday, Reagan campaigned in New Jersey and praised Sen. Bill Bradley (D-N.J.), a leading Democratic advocate of tax reform. But a Republican source close to the administration said the White House has done nothing to promote a bipartisan approach in the House, where the measure must originate and may face its toughest hurdles.

"We haven't had Rostenkowski down for a picture; we haven't shown any recognition that [House Speaker Thomas P.] Tip O'Neill [D-Mass.] gave useful testimony before the Ways and Means Committee," one official said.

Regan offered this view: "The special interests are all over Congress now every day. There is a continuing story of what's wrong, not what's right. There are very few people coming in and supporting it . . . . We're going to have to stay with the message."