LITTLE ROCK, ARK. -- Bill Clinton was running hard. He was on the run all week, moving swiftly through the third-floor marble corridor that links the House and Senate chambers in the state Capitol.

He was running after state legislators, "makin' deals" with them, which is how laws are passed here. He was running to enact a $21 million revenue package needed to meet the state's most immediate and pressing problems. And he was running, it is widely assumed here, for the 1988 Democratic presidential nomination.

Clinton, Arkansas' boyish-looking, 40-year-old governor, has been exploring a possible presidential campaign for months and intensified the effort after Sen. Dale Bumpers (D-Ark.) decided not to run. When he called the Arkansas General Assembly into special session last week, it was another step down that road.

"It is pretty hard to talk about responsibility unless you have exercised it yourself," he said.

Clinton is the third Democratic governor to ask himself whether he could continue as a state chief executive while running for president in 1988. The first, Mario M. Cuomo of New York, answered no. The second, Michael S. Dukakis of Massachusetts, said yes. Clinton, officially, has said maybe, but there is no doubt among his Democratic colleagues in the capitol building about his intentions.

"Sure, he is running," said Rep. Jodie Mahony.

"He's not doing much around here, so he might as well be running for president," said Nick Wilson, the president pro tempore of the state Senate and a frequent critic of Clinton.

Wilson's comments underscore why it is not easy for any governor to run for president. Unlike U.S. senators and House members, governors are expected to stay close to home, especially in a place like this, where the political style is highly personal.

The last sitting governor to win a major party presidential nomination was Illinois' Adlai Stevenson -- in 1952. The last sitting governor to be elected president was New York's Franklin D. Roosevelt in 1932.

In recent months, Clinton has been described as bored with his job as governor and distracted by his presidential ambitions and other outside duties -- which include the chairmanship of the National Governors' Association. The criticism has come even from such longtime Clinton allies as Mahony.

"My God, he's brilliant," Mahony said. "He has great ability to convince people of his position and a clear way of expressing it. I wanted him back here exercising those talents for the state."

Much of the criticism stemmed from Clinton's failure to win passage of major portions of an ambitious $180 million revenue program during the regular session of the legislature earlier this year. That left the state strapped for funds, necessitating the special session last week to enact what even Clinton described as a "Band-Aid" approach to the most pressing problems in the state's prison, welfare and higher education systems.

Arkansas' abiding economic problems present another potential hurdle for Clinton. Remote from the country's major population centers, the state is small, poor and rural. While Dukakis campaigns for the nomination by claiming to have produced an "economic miracle" in booming Massachusetts, Clinton told a joint session of the Arkansas legislature last week that "even if we can't go forward, we don't want to go backwards."

Arkansas also suffers from a deeply ingrained inferiority complex over its national image that was epitomized by a lengthy cover story in the June issue of Arkansas Times magazine titled "Will We Always Be the Barefoot State?"

The same attitude was echoed by Wilson when he suggested that the centerpiece of Clinton's administration -- a 1983 school reform program that included teacher competency tests and statewide standards for Arkansas' 330 school districts financed by a 1-cent sales tax increase -- has been overrated outside of Arkansas.

"Most people think it's a backward state and that this young man created the first education system we ever had and put shoes on everybody," Wilson said.

Although born to a poor, rural family, Clinton, a Rhodes scholar with degrees from Georgetown University and Yale Law School, does not fit the barefoot mold. At 32, he was the youngest governor in the country when first elected in 1978.

But two years later, Clinton ran into another Arkansas political tradition -- a tendency to resent politicians who appear to be growing "too big for their britches." He was defeated for reelection by conservative businessman Frank White, but regained the governor's office in 1982 and has stayed there since.

Local resentment of his national ambitions could hinder a Clinton presidential bid, but there is little evidence in the corridors of the state Capitol that this will be the case. Some legislators say privately that there was much more enthusiasm for Bumpers to run and represent Arkansas in the presidential sweepstakes.

"I don't see any great excitement" for a Clinton candidacy, said one.

Others, like Rep. Charles Stewart, say Clinton is too young to be elected and that, as the first Arkansas governor to win a four-year term since the 1870s because of a constitutional change, he should serve out the full term.

But the prevailing sentiment is that a national campaign by the state's bright, attractive and articulate young chief executive would only benefit Arkansas.

"The exposure for the state is what I like," said Rep. Bill Foster. "He'll never embarrass the state of Arkansas."

Clinton denies that he is bored as governor, but acknowledges having had "eight very tough months" since his reelection last November, as he juggled his state responsibilities with national aspirations.

His press secretary, Michael Gauldin, said Clinton "always seemed to a lot of people to be on his way somewhere else" and Clinton reinforced that image by recently telling Arkansas reporters that 1988 may be his only chance to run for president.

He did not, Clinton said later, mean to suggest that "I was in a panic to run," but was only trying to assess the current political situation. He said there is a good chance that a Democrat will be elected in 1988 and renominated in 1992, that he has no desire to challenge either of his state's popular Democratic senators, Bumpers and David H. Pryor, and that after 10 years on the job he is unlikely to run for reelection as governor in 1990.

"So you have to ask yourself what a fellow like me is to do out of elected office for six years," he said. "But I'm not distraught about it and I don't think that is a good reason to run."

If he does seek the nomination, Clinton said, it will be because "I thought I could carry a message to the country that would have a better chance of success and would be better either because of the message or the messenger."

Like the Democrats already in the field, Clinton said he would stress economic development and education. "The two major issues facing the country, apart from the issues of war and peace, which are always fundamental, are restoring worldwide economic growth, which I believe is a precondition for meaningful growth at home, and developing the capacities of our people better to function in a very sophisticated and tough world," he said.

But before he could devote much time to such national themes, Clinton had Arkansas' immediate needs to deal with. His popular school reform program is being fully implemented only this year but has already pulled the state closer to the national average in educational measurements.

Still, Clinton said, Arkansas ranks 49th among the states in teacher pay and 45th in expenditures per pupil. State employes have not had a pay raise in two years, and in half the school districts the teachers have gone without a salary increase for three years. Meanwhile, state officials are saddled with an antiquated constitution that requires a three-fourths majority in the legislature to raise the income tax, virtually eliminating that as a source of increased revenue.

Clinton estimated the state's real needs at $60 million, but after the troubles he encountered during the regular legislative session, he settled for the $21 million program that Speaker Ernest Cunningham told him was all the tax-resistant House would approve.

He worked hard all week to dispel the "bored and distracted" tag, prowling the Capitol corridors by day and working the telephone at night. By the end of the week Clinton had the extra $21 million, although not before he agreed to an accounting gimmick that will produce a one-time-only $9 million windfall by accelerating state sales tax collections this year. Another $5 million unexpectedly became available to the state because of changes in the federal income tax code, and Clinton quickly claimed it as part of the package.

Bob Wells, a reporter for the Arkansas Gazette, dubbed this "voodoo revenue," a reference to the 1980 Republican presidential primary, when George Bush described Ronald Reagan's economic program as "voodoo economics." Informed of Wells' remark, Clinton, who no longer discourages speculation about a presidential bid, didn't miss a beat.

"I guess that qualifies Bob to be my running mate," he said.