The Republican Party, betting that the economy will be the No. 1 issue on voters minds this fall, yesterday announced a nationwide "blitz" with "tax squads" crossing the country to promote a GOP-backed tax cut proposal.

The effort will be directed at selling Republican candidates and voters on the benefits of a tax bill introduced by Sen. William Roth (R-Del.) and Rep. Jack Kemp (R-N.Y.) that would lower personal income tax rates about one-third over three years.

Republican National Committee Chairman Bill Brock said the party will charter two jetliners for a September "blitz" in 12 to 18 cities around the country. The party has invited leading Republicans such as former president Gerald R. Ford and Ronald Reagan to join its tax squads.

In addition, a series of regional seminars is planned to persuade and inform Republican candidates about the Roth-Kemp bill which President Carter has said he would veto if passed by Congress.

"This is a major, significant issue, a clear division between the parties," Brock said. "We want to have our party and all our candidates speaking with one voice."

The Roth-Kemp bill, which has been endorsed by the GOP's national tax policy subcommittee, would provide substantial tax relief to persons earning more than 10,000 a year. Carter's program would concentrate most relief on people earning less than that.

The bill failed by 11 votes the one time it was offered on the House floor. But Republicans are banking that it will pick up new backing among Democrats who perceive a tax revolt sweeping the country in the wake of the California vote on Proposition 13 to reduce government spending.

"I think after Proposition 13 a lot of Democrats will support Roth-Kemp because they are concerned about their political futures." Brock said.

"We are not on the verge of a tax revolt; we're in the midst of one. The average American is angry," said Roth. "For the first time, they see themselves in a downward mobility. The American dream is no longer there."

Republicans, however, also have to worry about divisions in their own ranks among party members who are skeptical about cutting taxes without cutting government spending. Sponsors estimate that the Roth Kempt bill would mean a loss of $25 billion in government revenue a year.

Alan Greenspan, chairman of the Council of Economic Advisers under Ford, acknowledged the short-range effect of the bill could be inflationary. But he said that over two to three years, it would "create savings and investment," and "thus reduce the inflationary impact on the long run."

Under the proposal, a family of four with an $8,000 income would pay $12 instead of $120 in taxes; one earning $15,000 would pay $811 instead of $1,330; one earning $25,000 would pay $2,047 rather than $3,150, and one earning $40,000 would pay $4,512 instead of $6,848.

It would reduce corporate income taxes to 45 from 48 percent.