The White House, the biggest political arsenal available to GOP candidates this year, will provide only limited resources to the U.S. Senate campaign of Maryland Republican Lawrence J. Hogan, which some top GOP strategists have billed as "a long shot," at best.

Hogan's candidacy against incumbent Democratic Sen. Paul S. Sarbanes is not one of the White House's main priorities, according to top party strategists. It falls in a group of eight or nine Senate races in which the Republicans expect to win only one, and possibly two, seats in the Nov. 2 general election.

Although officials at the Republican senatorial campaign committee continue to tout Hogan's race as one of the most promising in the nation, a senior GOP political planner said that by nominating Hogan the party had squandered an opportunity to unseat a vulnerable Democrat in Maryland. He described the Hogan campaign as "way down at the bottom of the list" of the Senate races that are getting White House attention.

President Reagan will campaign in Virginia next week on behalf of U.S. Senate candidate Rep. Paul S. Trible, for example. But the president will not make any trips to Maryland, except to fly in and out of Andrews Air Force Base, eight miles from Hogan's office in Upper Marlboro, before the election, according to these party strategists.

"It's not the case that Hogan has been completely written off," said one leading Republican planner, "but it is certainly not one of our best shots. His campaign is in a category where it's a long shot, but there's still a chance. To maintain that status as a long shot, he has to raise a lot of money quickly."

Hogan visited the White House Friday for a picture-taking session with Reagan and said the president was distressed when Hogan informed him that unnamed GOP strategists were giving the impression that the Hogan race was not important. Hogan said that Reagan threw up his hands and declared: "Heads should roll on this one."

Vince Breglio, political director of the senatorial committee, said that he lends no credibility to political assessments by "unnamed sources."

"The White House is full of people who speak behind closed doors," Breglio said. "I suspect there are other motives at play. The one race where Republicans have been feeding off their young is Maryland. And it involves people in the White House and inside the state. I haven't found a Republican yet who doesn't have an axe to grind in Maryland. Part of it is because Larry Hogan is a maverick Republican who has ruffled the feathers of some establishment Republicans. But his race is one of the five or six most winnable challenge races in the country."

Some stalwart Republicans, including several top GOP strategists, still bear a grudge against Hogan because he called for the impeachment of President Nixon while serving on the House Judiciary Committee in 1974. Other party members became annoyed with Hogan last year when, they say, he pushed his son, Lawrence Hogan Jr., to run for the 5th Congressional District seat vacated by the ailing Gladys Spellman, a race Hogan Jr. lost in the primary. Hogan maintains that he tried to discourage his son from running.

The limited White House involvement in the Hogan campaign, according to the GOP strategists, is based partly on a premise that the president will only venture into states where a Republican has a good chance of winning and where the voters are not hostile to Reagan's programs.

Maryland, one of the six states that Reagan lost in 1980, has a 3-to-1 ratio of Democratic voters, many of whom are blue-collar. The state government is dominated by Democrats, with Gov. Harry Hughes leading a strong Democratic ticket in his bid for reelection this year. Compounding the problem for Reagan and Hogan is Maryland's high unemployment rate, which is close to 10 percent. Virginia, by contrast, gave Reagan overwhelming support in 1980 and its voters traditionally have shown a greater predilection for conservative Republican politicians.

"The president doesn't want to put himself in a position of having a negative batting average," said one Republican party official. "Risky is too mild a word for a Reagan trip to Maryland . It would be suicidal."

So far, in addition to the picture-taking session Friday, Hogan has received a personal fund-raising letter from Reagan and has had meetings with his top political operatives. But to date, Energy Secretary James Edwards is the only cabinet member who has been involved in his campaign.

Hogan has invited Vice President George Bush to come to Maryland, but Bush has not made a firm commitment. Bush appeared yesterday at a bull roast in Annapolis for Rep. Marjorie S. Holt, the state's only Republican member of the U.S. House. Details on Page B1. Last week his aides stressed that he was "not ducking Hogan," and Bush took pains yesterday to single Hogan out for praise, along with GOP gubernatorial candidate Robert A. Pascal. Both were seated behind Bush and Holt on the stage.

"Larry Hogan is a doer, he's a scrapper, and I guarantee he's going to give Sarbanes a run for his life," Bush said. "Send my friend Larry Hogan back to the Senate and you'll see that place come alive."

But Bush said afterward he doesn't know whether he will come to Maryland to campaign for Hogan. "I hope so, but I don't know because we're on the darndest schedule you've ever seen," Bush said.

Hogan's campaign manager, George Nesterczuck, said that Transportation Secretary Drew Lewis will attend a reception for political action committees that Hogan has scheduled next week. The names of four cabinet secretaries appear on the invitation, Nesterczuk said.

As part of an overall strategy to preserve Republican control of the Senate, the White House has been willing to use its best resources, Reagan, Bush, former president Gerald R. Ford, Treasury Secretary Donald Regan and Lewis, even in cases where the Republican candidate is not a close ally of the president.

Reagan has campaigned on behalf of Rep. Millicent Fenwick in New Jersey, for example, and the White House has embraced the candidacy of Sen. Lowell Weicker, a liberal Republican from Connecticut. Last month, despite public differences with U.S. Senate candidate Pete Wilson in California, Reagan appeared at a fund-raiser in Los Angeles and in one evening raised $1 million for Wilson's campaign.

In Maryland, Sarbanes was and still is viewed as beatable by the GOP, but some party officials believe Hogan is "carrying a lot of baggage" as a result of past conflicts within the Republican Party and has a negative image among many voters.

"I think the negatives are very important," said one official. "Hogan has incredible negatives. So does Sarbanes. But there is no question that Hogan was not the first-choice candidate for that race."

Some GOP planners say that Holt, a staunch conservative from Anne Arundel County, would have been the best hope for a Republican challenge to Sarbanes because she has a less controversial image than Hogan and would have had better success in raising money. She had considered entering the race, but last year decided against it.

Breglio, of the senatorial committee, disputes these views and insists that the negatives in Hogan's campaign are no worse than those of Sarbanes. Paul Russo, who works in the White House political operations office, says the race is still "volatile" and that "in a few weeks from now, we're going to have quite a different picture."

Hogan, concerned that his efforts to raise money will be undermined by impressions that the White House is not solidly behind him, contends that his critics are "operating with faulty data."

Although some Republican officials believe that a visit to Maryland by Reagan or other top-ranking White House officials would be embarrassing for Hogan in a state so openly hostile to the president, it is a vital ingredient in successful fund raising.

In wealthy Northern Virginia, for example, Republican Rep. Stanford Parris amassed $130,000 for his congressional race after visits by Bush, Regan, and Lewis. Bush appeared at a $1,000-a-person cocktail party and Regan attended a breakfast at the Belle Haven Country Club. Rep. Frank Wolf raised about $84,000 after visits by presidential adviser Edwin Meese III, Regan, and Lewis. Bush, Regan and Lewis also have made personal appearances on behalf of Trible, the Senate candidate.

Despite the White House's low profile in Hogan's campaign, the Prince George's county executive has received money, personnel, and strategic advice from the senatorial committee, including a pledge of $230,000 to be spent on his campaign.

And last week he was the only candidate not currently a congressman or senator who was invited to speak to the Republican Senate Trust Committee, a group of wealthy donors, each of whom has given at least $10,000 to the senatorial committee. At the end of the day, Hogan dined at the vice president's home with members of the Trust Committee.

"We came out of the session with some checks in our pockets," said Nesterczuk, Hogan's campaign manager.