Stressing the familiar theme that "government alone is not the answer" and that private efforts must be strengthened to pick up the burdens that government should not or cannot handle, President Reagan this week challenged the United Way of America to double its $2.3 billion annual collections over the next few years.

United Way Chairman James D. Robinson III has agreed to pick up the gauntlet.

Only a year ago the United Way and other charitable groups were fiercely criticizing the Reagan administration over Treasury plans for sharp cuts in charitable deductions under the federal income-tax laws.

While the tax fight has not been forgotten, the proposals have since been softened, and all was sweetness and light Tuesday as President Reagan and Nancy Reagan, in a meeting with United Way leaders, agreed to serve as honorary chairmen of United Way's centennial in 1987.

Despite the dispute over the tax proposals, Reagan has had a long and close relationship with United Way, serving as its national spokesman as long ago as 1961. Nancy Reagan was national women's chair from 1969 to 1971.

Robinson, voluntary chairman of United Way and chairman and chief executive of American Express, said that the goal of doubling collections over the next five years had been developed by United Way, but that Reagan was challenging the group to do it more quickly.

Since early in the administration, officials have said that as the government cuts back on some of its functions, charitable organizations should take up some of the slack.

In fact, statistics obtained from United Way and the charitable group umbrella organization Independent Sector show that collections by United Way rose from $1.526 billion in 1980 to $2.33 billion in 1985, outpacing inflation.