Backers of last year's failed tax initiatives expect to have a new petition calling for an end to taxing food sales ready to file with the state by the end of next week.

And a second petition to raise the state's minimum wage from $2.50 to the same level set by the federal government, $3.35, is also likely to be filed by the Tax Limitation Coalition.Joining the group behind the three tax-cutting measures defeated at the polls last November are leaders of the state Democratic Party and the state AFL-CIO.

The unlikely alliance between the conservative members of Utah's tax-protest movement and two of the state's most liberal groups is the result of their combined frustration with the Republican establishment.

All three factions believe working together can accomplish what they were unable to do alone, either through the initiative process or at the Legislature.

"We don't have the power," state Democratic Party Chairman Randy Horiuchi said. "What we have to do is take a lesson from our friend, Merrill Cook, and go to the people."

Democratic leaders, always looking to bolster their meager ranks, have been trying since the last election to attract tax-initiative supporters into the party.

Organized labor is being brought into the effort by Horiuchi, who came up with the idea for raising the state's minimum wage. AFL-CIO head Ed Mayne said he agrees the petition process is the only route left.

Both Mayne and Horiuchi can recite a long list of issues affecting their constituents, including removing the sales tax from food, that were either ignored or rejected by legislators in 1989.

And although the AFL-CIO, which represents some 68,000 Utahns, came out strongly against the tax initiatives last fall, Mayne said he is excited about using the petition process to benefit working men and women.

Cook, who unsuccessfully ran for governor as an independent, said the cooperation among the groups is making it easy for him to set aside his plans to start a third political party - at least temporarily.

Those plans are on hold until he can see if what he termed a "fragile coalition" can hold up through the lengthy process of getting the initiatives on the ballot of the next general election, which won't be until November 1990.

Before the sales tax petition can be filed with the lieutenant governor, supporters must decide whether they want sales tax to be taken off food all at once or over a two-year period to ease the effect on government.

Cook and others in the coalition want food sales to be tax-free as of Jan. 1, 1991. But Democrats want only half the tax removed the first year after the next general election.

Horiuchi and Cook are scheduled to meet to resolve the issue this weekend.

Filing an initiative petition with the lieutenant governor's office is the first step to putting the issue before voters. A petition cannot be circulated until it also has been reviewed and approved by the attorney general's office.

To qualify the issues for a spot on the next general-election ballot in November 1990, nearly 65,000 qualified voters will have to sign the petitions before June 8, 1990.