The streets of this working-class Detroit suburb are named for the automobiles that control the fate of most of its residents. In the homes on Dodge Avenue, you learn very quickly why President Carter may have a hard time carrying Michigan this year.

Dodge Avenue is in Roseville's Precinct 2, which Carter won with 62 percent of the vote in 1976, even while losing both surrounding Macomb County and the state of Michigan to Gerald R. Ford by roughly 53 to 47 percent.

This year, Carter's opponent is not Michigan's favorite son Ford but Ronald Reagan, drubbed by Michigan Republicans in both the 1976 and 1980 primaries and more conservative than any Michigan election winner in many years.

For that reason, Michigan is at the top of the target list of "Ford states" Carter hopes to carry this year, in order to build a cushion against threatened losses to Reagan in states such as Texas, Mississippi and Missouri, which he won last time.

To carry Michigan, Carter will have to boost his margins in places such as Roseville. But on Dodge Avenue today, instead of gaining support, he is suffering a fearful rate of attrition.

In half of the homes one visits, a member of the immediate family has been out of work in the last year. Betty Billings is one of the lucky ones, because her husband works for the Roseville Park Department and has not been laid off.

But the 49-year-old housewife is switching to Reagan. And that is bad news for Carter, because she is not the kind of voter he should be losing. She is a Democrat by inheritance, considers herself "more on the liberal" side of the spectrum. She thinks Carter might be more effective in dealing with Congress than Reagan because "he's probably learned some lessons by now."

And on the "peace issue" that Carter is not-too-subtly using to stir fears about Reagan. Betty Billings is receptive. She thinks Carter would be better at dealing with hostile foreign governments, because "his approach is a little softer."

But her real worry is the economy. "There are so many out of work here," she said, "it's heart-breaking. The kids coming out of high school can't get jobs and their parents can't afford to send them to college so they sit around -- and the next thing you know, there's crime in the neighborhood like we never had before."

"I truly believe this inflation is Carter's fault. We never had prices going up like this before he became president. He seems to take his advice on everything from people who don't know what they're doing, and he doesn't seem to have enough conviction to rely on his own judgment," she said.

And then she mentioned another topic that seems to rankle many in this heavily Catholic, unabashedly patriotic suburb: the hostages in Iran.

"He had advice that might happen if he let the shah in," Betty Billings said, "but he listened to the people who told him to do it. And then he let it get out of hand." Like a startling number of her neighbors, she knows from the TV news shows exactly how many days the hostages have been held. "Now," she said with contempt in her voice, "you hear that he's going to do something before the election to get them out. If you ask me, he could have done something a long time ago."

Betty Billings is one voter among the millions, but the pollsters and politicians find her attitudes anything but unusual. "There is a direct-line correlation," said Robert Teeter of Detroit's Republican-oriented Market Opinion Research Co., "between concern about the economy and the propensity to vote for Reagan."

Sam Fishman, chief Michigan political operative for the pro-Carter United Auto Workers, said, "In Michigan, Ronald Reagan is right: there is a depression. So the incumbent starts out with a huge negative. When Carter offers an economic package for next year, people say, 'Why don't you do it now?'"

As Fishman noted, "most of the people laid off are Democrats. Many of them will not vote at all, because the unemployed are the most alienated. And some will vote vindictively."

Vindictiveness is not the word the people on Dodge Avenue use to describe their mood, but many of them concede they are very, very angry.

Cathy Bowles, wife of a Chevrolet draftsman and not old enough to vote in 1976, thought "the first couple years with Carter were pretty good. But this last year, anything he's touched has turned bad. He can't straighten out his brother. He can't rescue the hostages, and he's sure showed he can't handle the depression."

Bowles' mechanic brother has been off work for a year and she is angry that the government seems to be worrying about other people's problems, not those of people like her brother. "They let the Japanese bring their cars in here. They let the Cubans send us all the people they can't feed, so the welfare lines just get longer. They should stop all that."

Bowles says she will cast her first presidential vote for John Anderson.

Arthur Ketelhut, 31, has been surviving on a part-time CETA job as a handyman at the high school since he lost his construction job last November. "I'm a Democrat," he said, "but this time I'm probably going to change. I don't know why Carter doesn't start something like that CCC program they had in the [1930s] depression, so guys like me could build some buildings or plant some trees or do something useful."

Another thing disturbed Ketelhut: "I was in the Navy from '76 to '78 and everywhere I went, I saw the Russians. It's unbelievable how they're building up, and Carter doesn't seem to do anything."

Ketelhut said he was "probably a Reagan" voter, but said, "I want to hear more about what Anderson's got to say."

If Dodge Avenue's 30 percent defection rate among Carter's 1976 supporters were projected to other blue-collar, white neighborhoods, Carter's chances of recapturing Michigan and its 21 electoral votes from the GOP column would be nil.

But there are problems for Reagan as well, and they become visible when one moves from blue-collar Roseville to the more affluent homes on Elmhurst Avenue in Royal Oak, perhaps 12 miles west.

Oakland County leans Republican, but it is prime ticket-splitting country.

The 33rd precinct in Royal Oak, of which Elmhurst Avenue is a part, gave Gov. William G. Milliken (R) 79 percent of its votes in 1978, and he was reelected handily. That same day, its voters cut Sen. Robert P. Griffin (R) back to 62 percent support -- and he lost his bid for another term.

Carter, who got only 36 percent of the vote here in 1976, has lost some supporters. Patti Behling, 28-year-old bookshop employe, is switching to Anderson because the president seems to her "all talk and no action."

But down the street, R. J. Molloy, a 68-year-old retired marketing manager, who voted comfortably for Ford last time, is "disappointed" in this year's field. Reagan's only qualification, he said, "is that he takes advice from some knowledgeable people. But," he added, "if he shoots his mouth off stupidly once more, he's dead as far as I'm concerned. That remark about the klan was stupid. Sending his friend Bush to China when he [Reagan] is saying what he was saying about Taiwan was stupid. If he keeps that up, I'd vote for Anderson -- purely as a protest."

And a 50-year-old neighbor, a "very conservative" Catholic who declined to give her name, said she voted for Ford last time but "will probably stick with Carter. I'll give him four more years, rather than start new with Reagan. I just think of him as a movie star."

The Anderson factor on these streets shows up in the polls -- particularly in the ticket-splitting precincts, among younger voters and in the college towns like Ann Arbor and East Lansing. Leaders of both parties were startled to find that 93,000 people voted for Anderson in the August primary, thereby qualifying him for the November ballot while denying themselves the opportunity to vote for local candidates in either the GOP or Democratic primary.

A commercial poll taken during the week of the Democratic National Convention showed Anderson with 22 percent of the Michigan vote, compared to Reagan's 31 percent and Carter's 29 percent. A more recent private poll showed Anderson had dropped into the teens, while Reagan had moved up to a lead of five or six points.

But both sides see Michigan as a state that is still to be won, and they are mobilizing for a massive, multi-million-dollar effort.

While Carter and Edward M. Kennedy split the Michigan delegation 50-50 at the August convention, the Democrats here have come together more rapidly than in many other states, in large part because United Auto Workers president Douglas A. Fraser and his deputies, who provided the organizational muscle for the Kennedy drive, were moving toward reconciliation long before the convention met to ratify Carter's victory.

Morley Winograd, former state Democratic chairman and a leading Kennedy backer, was named a Carter elector last month -- and there have been other gestures of harmony.

The UAW has cranked up its propaganda mill, taking roundhouse swings at Reagan's labor record and economic stands and plugging "Carter's plan for jobs."

"We'll do the traditional things," Sam Fishman said, "but how efficient it is this year remains to be seen."

While the union leadership seems persuaded that Reagan represents the threat of "a sharp right turn" in economic and social policy, and while Fraser and others are longtime supporters of Vice President Mondale, even UAW spokesmen have a hard time sounding convinced that Carter's policies spell better times for the auto workers.

"We're starting earlier this year than we usually do with our mailings and leaflets," said Don Stillman, the UAW public relations chief, "because we know we've got a lot more persuading to do."

If the Carter forces are welcoming help from Fraser and other Kennedy backers, Reagan is at least as glad to have the backing of moderate Republicans who joined Gov. Milliken in giving George Bush a convincing victory over Reagan in the early-May presidential primary.

With Bush now on the Reagan ticket, the Reagan staff has gone out of its way to accommodate Milliken.

The firebrand conservative who was leading the Reagan campaign was replaced with John Gnau Jr., a businessman who started in politics with Milliken's original mentor, ex-governor George Romney. Lorette Ruppe, a Bush supporter, was named cochairman of the revamped campaign. Similarly, at the staff level, the executive director is a Reagan man and the field director a former Bush aide.

Both campaigns are counting on the state parties to do much of the vital voter identification and turnout job. During his visit last week, Reagan raised $200,000 in contributions of $5,000 to $25,000 toward the GOP state committee budget of $1.3 million for phone banks and precinct work. Democrats say they are promised similar help from Mondale and Carter campaign chairman Robert S. Strauss in meeting their more modest $350,000 budget.

The disparity in strength is not as great as the numbers suggest. Carter will also enjoy the backing of the UAW, the state AFL-CIO and the Michigan Education Association. Detroit Mayor Coleman Young, an early supporter of the president, will put his considerable muscle behind an effort to mobilize a heavy black vote in the city.

But Milliken, whose strength has been demonstrated repeatedly in the suburban ticket-splitting counties where Michigan elections are usually decided, has surprised even old friends by his apparent readiness to go all-out for the Reagan-Bush ticket.

An outspoken progressive Milliken made no effort to disguise his disagreements with Reagan during the six years they attended governors' conferences together. In 1976 and 1980, he led crusades to deny victory to the Californian in Michigan's presidential primaries.

But, in introducing Reagan at the Michigan State Fair on Labor Day, Milliken said, "I have come to like and respect and admire this man" -- words that delighted Reagan and his organization.

"The strategy for Reagan winning this state," said Mel Larsen, the state GOP chairman, "is for him to campaign for blue-collar voters and still be closely identified with Bill Milliken, who has tremendous credibility with the ticket-splitters."

Milliken said in an interview that he would help by "appearing with Reagan and Bush whenever possible in the state and giving them whatever advice and help they want. So far, they've been very receptive.

"Quite candidly," he said, "the fact that Bush is on the ticket and there are a great many Bush people in the organization makes it easier for me."

Milliken joined other Great Lakes governors 10 days ago in telling Reagan to stop his controversial ad lib comments about China policy and the Vietnam war and get on to "positive proposals" about the economy.

"If he does that," said Milliken, "I think the odds are that he can carry Michigan."

The political influence Milliken can mobilize to make that prediction come true is one more problem Carter faces in salvaging this state.