Sen. Howard H. Baker Jr., presidential hopeful, Republican star of the Watergate hearings and minority leader of the U.S. Senate, sent out a doomsday letter a couple of weeks ago to, as they say in politics, 5,000 of his closest friends.

It was a desparate plea for cash, $116,826,50 to be exact. "There's never been a time in my political life when I needed your help more than I need it now," Baker wrote. "Mistakenly, many of my supporters believe I have already won reelection."

Within days, tens of thousands of dollars had poured into his headquarters, enabling Baker to buy the television time he said was needed to keep his campaign from going down the tube.

The letter's dramatic language makes a telling point.

Basically, Baker, one of the Republican Party's brightest hopes for 1980, faces two major problems in his attempt to win reelection to a third term in a big way and keep his presidential hopes alive.

One is his support of the Panama Canal treaties, which outraged many Tennessee voters. The other is a failure on the part of many, until recent weeks, to take his opponent, a politically unknown housewife, seriously.

Baker, polls indicate, still leads in the race by a comfortable margin, and will likely win if present trends continue.

But there is a danger, as a Democratic senator said, that. "when that woman gets through with him, Howard Baker isn't going to look like a presidential contender."

"That woman" is Jane Eskind, a 45-year-old Democratic Party activist from nashville, who visited this small Appalachian mountain community a few days ago.

Eskind, a member of the Democratic National Platform committees in 1972 and 1976, was virtually unknown when she announced her candidacy June 5.

But she has proven to be an able, articulate and energetic campaigner. She is also very rich - rich enough to pump $625,000 of her own money into the race.

A liberal by repurtation, she's running almost as an Archie Bunker conservative, who opposes the Panama Canal treaties and supports pork-barrel projects for Tennessee and prayer in public schools.

Baker has lost tough with Tennessee during his 12 years in Washington, she claims. He now practices "the politics of personal ambition at the expense of the people he was sent to TR FOR ADD THREE represent."

This is the same Tennessee tactic that was used to defeat Democratic Sen. Albert Gore in 1970 and, to a lesser extent, Sen. William Brock, now the Republican national chairman, in 1976. But Baker claims it won't work against him because he has spent 142 days in Tennessee this year, and has five offices in the state to keep him abreast of local concerns.

His strategy is to ignore Eskind as much as possible, and hope voters do the same. He has refused to debate or appear on the same platform with her. And he only reluctantly replies to the daily charges she levels.

The closest Baker has come to open criticism came last week after Eskind accused him of "lying" when he said an amendment he co-sponsored to the Endangered Species Act would save the controversial snaildarter-bedeviled Tellico Dam in East Tennessee.

"I don't recall that any candidate for statewide office, Republican or Democrat, has ever made that charge before - that their opponent was a liar," he said in an interview. "The level of this campaign has reached such a point that my only advice to her is to calm down, just calm down."

Baker, 52, is clearly looking toward 1980 as he moves around Tennessee in the last days of autumn. He rarely makes a stop without being introduced as "the next president of the United States," or being asked about his ambitions.

Indeed, he sounds more like he's running against Jimmy Carter and the Democrats in Congress than Jane Eskind. His speeches are partisan, but not too much so, for a key to Baker's success has always been his appeal to Democrat and independents as well as GOP stalwarts.

He rails against inflation - "the biggest unpunished crime in the country." He frets about the Soviet Union gaining the upper hand militarily. He hints about leading a fight against the second strategic arms limitation treaty with Russia.

It all sounds very cosmic, very presidential. A Baker for President campaign would hinge largely on circumstance: Carter's popularity (he thinks it will drop in six months); whether Gerald Ford and Ronald Reagan will be candidates (he thinks they are both too old but will run); the size of the Republican field (he thinks it will be large and halt will work to his benefit); what his family thinks; and, of course, what happens this fall.

Baker whose father and stepmother, both served in Congress, has led a charmed political life. After losing his first race for the Senate in the 1964 Goldwater debacle, he won election handily in 1966 and 1972 by a 56 and 61.5 percent margin respectively.

But private polls by both candidates in recent weeks showed him leading by a surprisingly slim 10 percent.

Baker insists this won't matter. "I've never said I wanted to win by a large margin," he says. "I just want to win. People forget about the margin the day after the election."

His biggest liability is the Panama Canal treaties. His support was a critical factor in their passage, something that enhanced his national image as a statesman. But many voters, particularly conservative Republicans in his home area of East Tennessee, have never forgiven him.

When he arrived at a rally at the University of Tennessee in Knoxville last Wednesday, for instance, Baker was greeted by a dozen protesters carrying "Remember Our Canal" placards.

When Jane Eskind visited the Sweetwater City Hall here two days later, Scott Holder, a clerk in the pub- [TEXT OMITTED FROM SOURCE]