The Business Roundtable, one of the nation's most powerful business lobbying groups, today is expected to consider whether to throw its support behind a national advertising campaign calling for a dramatic shift in federal tax and spending policies.

The Roundtable will take up the stern budget-cutting recommendations of another group--called the bi-partisan budget appeal--which is planning a publicity drive to push for lower deficits and higher taxes, sources said yesterday. Many Roundtable members already have lent their names to the ad campaign, which is being organized by Peter G. Peterson, a former Commerce Secretary under President Nixon.

The group has drafted an advertisement--originally intended to run in The Washington Post, The New York Times and the Wall Street Journal on Jan. 25--in which there are detailed recommendations for cutting about $175 billion from the 1985 budget deficit. However, not all of the potential signatories listed on the draft of the advertisement have yet agreed to its form or the detailed proposals, sources said.

A spokesman for the Roundtable said yesterday that today's meeting was one of a regular series at which many topics would be considered. He said, however, that one of the topics on the agenda was tax and budget policy. He said that within that category the group will consider the "Peterson initiative," adding that it would be unusual for the Business Roundtable to endorse an advertisement of the kind being planned.

The Roundtable may, however, issue a policy statement on taxes and spending after its meeting. Last year, it issued several budget statements, and eventually endorsed the tax increase which was enacted last summer, the spokesman said.

Peterson's group--which has five former treasury secretaries among its founding members and several hundred initial supporters from the leaders of the business and financial world--wasestablished last year in an attempt to push President Reagan and Congress into cutting the huge projected budget deficits. The group plans to hold press conferences and undertake personal lobbying in addition to placing the advertisement, sources involved in the campaign said last week.

The draft advertisement circulated by Peterson describes the federal budget as "now out of control" and proposes strong measures to correct the deficit. Many of these run counter to the president's unwillingness so far to cut his defense spending buildup or to agree to further tax increases. For example, the draft proposes a cut in defense spending of $25 billion in 1985 with tax increases of $60 billion, and $60 billion of cuts in domestic programs.

John Albertine of the American Business Conference--who has been a supporter of the appeal so far--said yesterday that his organization will not support the appeal if it calls for new tax increases, over and above the 1982 tax increase bill. The fact sheet of proposals was originally circulated last summer, he said, before the passage of the tax bill. Albertine's group eventually supported the tax measure on the basis that this would be the last tax increase.

After the contents of the draft advertisement became public last week, some of the potential signatories reportedly felt uncomfortable about the implicit criticism of the White House, sources said yesterday. Peterson said last week that he did not expect the general thrust of the draft proposals to be changed, although the number of signers might.