Michigan voters dealt a sharp blow to the national tax-cutting movement yesterday as an initiative to strip state lawmakers of the power to raise taxes was defeated by a projected 2 to 1 margin.

Michigan was one of four states -- along with California, Nevada and Orgeon -- where the 1970s tax revolt had resurfaced this year. But a huge early lead in the polls rapidly dissipated as Michigan's political establishment -- from Gov. James J. Blanchard (D) and business leaders to the AFL-CIO and the big auto companies -- mounted an expensive campaign against the proposal.

Opponents picked up momentum in the last two weeks as Blanchard was joined by former Republican governors William Milliken and George Romney in a television ad contending that the Voters Choice measure would cripple the state. Blanchard called the anti-tax measure "Voter's Fraud" and said it would make Michigan "the credit deadbeat of the nation."

In the rest of a grab bag of state and local referenda yesterday, Missouri and West Virginia approved state-run lotteries, while a Missouri measure to restrict utility rate increases and an equal rights amendment in Maine were headed for defeat.

The Maine amendment was identical to the proposed U.S. constitutional amendment. The battle had been neck and neck until the state's Roman Catholic diocese came out against the amendment, and leading bishops urged their parishioners to vote it down in sermons last weekend.

The measure, pushed hard by Gov. Joseph E. Brennan (D), said that equal rights "shall not be denied or abridged in this state because of the sex of the individual." Church and antiabortion leaders argued that it could legalize homosexual marriage and require public funding of abortions, according to Initiative News Report.

In Missouri, a measure to restrict utility rate increases and disposal of nuclear waste was headed for a substantial defeat. Missouri utilities mounted a multmillion-dollar ad campaign to defeat the initiative, which would have barred them from charging consumers for construction cost overruns, repairs on defective power plants and a new reactor expected to generate excess capacity.

Proposals for state-run lotteries, among the legalized gambling initiatives in six states, were heading for victory in Missouri and West Virginia. A West Virginia measure to allow voluntary prayer in schools also was assured of passage.

The more than 200 questions on state and local ballots ranged from Utah's proposal to keep pornography off cable television to Washington's effort to overturn treaties giving Indians special salmon-fishing rights. Other proposals called for raising revenues through legalized gambling, keeping pornography off cable television and banning nuclear weapons.

The Michigan measure, like many of the other most controversial initiatives, involved political consultants who employ the same tools used to sell candidates -- telephone banks, targeted mail, slick television ads and multimillion-dollar fund-raising drives. But the battle was over a clash of ideas, not office seekers.

The Voters Choice measure would have rolled back Blanchard's 1983 income tax increase, required a referendum for any future tax hikes and forced governing bodies to muster a four-fifths majority to raise licensing fees or tuition.

Blanchard and his allies said the initiative would cause thousands of layoffs, decimate state schools and colleges, threaten toxic waste cleanup efforts, hurt programs for the elderly, choke off new business and force cities to cut back on basic services. Proponents, led by Blanchard's 1982 rival, Richard Headlee (R), called this a scare tactic.

Michigan voters turned thumbs down on the measure even while giving a strong majority to President Reagan, in part because of adverse reaction to Democrat Walter F. Mondale's call for a national tax increase.

Nevada's anti-tax measure would require a two-thirds vote by both the legislature and the public before taxes could be raised. A spokesman for Gov. Richard Bryan (D) called the proposal "a nightmare."

California's initiative was written by Howard Jarvis to extend the reach of his successful 1978 referendum issue called Proposition 13. It would require a two-thirds legislative vote for new state taxes and a two-thirds popular vote to boost local fees and taxes. But the new Jarvis measure would give a large tax rebate to residents who bought their houses before 1977, while those who purchased homes after that date would face a tax increase.

Oregon voters faced a plan to impose a strict ceiling on local property taxes; four other states were voting on tax-rollback measures.

Oregon, California, Missouri also were seeking to raise money by authorizing state lotteries. The gambling industry was not leaving the outcome to chance; the campaign for a California lottery was funded mainly by Scientific Games, a Bally Inc. subsidiary that makes lottery equipment.

Casting an envious eye on Atlantic City's gambling glitter, Arkansas and Colorado were voting on whether to legalize casino gambling in designated communities.

In Arizona, newspaper exit polls showed voters rejecting several initiatives to control health care costs. One set was proposed by the business community in an effort to hold down health insurance premiums, while the other was backed by the hospital industry.

More than 1,300 Arizona companies, including such large employers as Sperry Inc. and Motorola, drew up an initiative that would allow the state to regulate health facilities and would set up an independent agency to oversee health planning and budgeting.

The Arizona Hospital Association accused the companies of "legislative terrorism" and offered alternative initiatives that would limit hospitals' revenue for five years and place a short-term freeze on rate increases and new hospital beds.

The corporate coalition aired commercials showing rows of empty beds to highlight Arizona's 54 percent hospital occupancy rate, well below the national average of 71 percent. The hospital industry countered by warning of a big state bureaucracy overseeing second-class health care.

Abortion-financing bans were on the ballot in Washington and Colorado.

Utility companies spent approximately $1 million fighting a Missouri initiative that would limit annual rate increases to 10 percent. The measure also would bar them from charging consumers for construction cost overruns, excess capacity and repairs on defective power plants. Fueling the debate is a nearly completed nuclear plant that may generate more electricity than the state needs. Utilities also fought an Oregon measure that would create a "citizens utility board" to oppose proposed rate increases.

Sixteen communities were voting on whether to declare "nuclear-free zones" within their borders, including Ann Arbor, Mich. and Santa Monica, Calif. South Dakota, meanwhile, was voting on a nonbinding freeze on nuclear weapons.

California, as usual, was fielding a full complement of initiatives. The Democratic leadership was fighting two measures that would limit all campaign contributions to $1,000 and take political redistricting out of politicians' hands. In response to complaints of Democratic gerrymandering after the 1980 election, the proposal would name a panel of retired state judges to draw political boundaries; critics say this would politicize the judiciary.

Other ballot measures yesterday, according to Initiative News Report, would end Montana's regulation of milk prices and reaffirm the right to bear arms in North Dakota and Utah. East Detroit, Mich. was voting on whether to change its name to Erin Heights to avoid association with Detroit.