From their suites of offices at One DuPont Circle in Washington, the leaders of the nation's $60-billion-a-year higher-education industry are launching a grass-roots lobbying campaign against the Reagan administration's coming round of deep cuts in multibillion-dollar student financial aid programs.

The fiscal 1983 budget won't be made public until Feb. 8. But the college lobbyists already are at work because they hear Reagan will propose cutting Pell grants for needy students from the current $2.6 billion to $1.4 billion, knocking one million students off the rolls.

They also predict that $1 billion in campus work-study and other direct aid will be cut in half, and that graduate students will be shut out of the guaranteed student loan program. About 600,000 graduate students, more than half of the graduate enrollments, depend on such loans to finance their education, according to the American Council on Education.

A coalition of 12 groups called the Action Committee for Higher Education has scheduled a news conference Tuesday and is flooding the mails with information packets containing the dreary numbers and a "counterattack checklist." The strategy suggests college presidents mobilize students, parents, alumni, their local media and, above all, their congressional delegations.

Jack Peltason, president of the umbrella American Council on Education, said college groups have lobbied before, but never in such a coordinated or intense way. It was only in recent years that college administrators got over the feeling that it was "inappropriate to take part in the political process," he said.

Thomas W. Linney Jr., lobbyist for the Council of Graduate Schools, said college leaders for years have had the "classic ivory tower mind-set," willing to debate great issues, but not to take an active part. There are no political action committees in higher education as there are among the teachers' unions on the elementary-secondary level, he noted.

There also have been tensions between the different higher education groups--public against private, two-year against four-year institutions--trying to protect their part of the federal aid package.

This time round the college groups will be united and politically active, Peltason promised in a recent interview. "We're saying, 'Hey, fellas, this isn't just minor tinkering. This is dismantling the whole structure of student financial aid.' "

Peltason also said that the cuts would fall "disproportionately on the poor. Education is not quite so price-sensitive for the middle and upper class. But we've just been beginning to make progress in having the disadvantaged and minorities think of the possibility of college. These cuts would slam them back 15 or 20 years."

The budget cuts in student aid are particularly noticeable because they follow a decade of huge jumps in such federal support, and they come at a time when the country's 3,000 colleges and universities are strapped with higher costs and the prospect of declining enrollments.

Edward M. Elmendorf, the Department of Education's chief financial aid official, outlined the growth for a House subcommittee hearing last week. He noted that when Pell grants began in the 1973-74 academic year, they reached 185,000 students and cost $122 million. This year they serve 2.8 million students and cost $2.3 billion.

Another $1 billion now goes to 1.5 million students for campus work-study, supplemental grants and direct loans, Elmendorf said.

But the whopper of the student aid programs is that for guaranteed student loans. In fiscal 1981, he noted, 3.5 million students obtained $7.7 billion worth of loans. The direct cost to the Treasury, because the government pays banks an interest subsidy, was $2.5 billion for fiscal 1981, and is projected to top $3 billion for this year.

Since the portfolio of loans totals more than $20 billion, he added, every 1 percent increase in the interest on Treasury bills costs the program $200 million.

What the administration views as out-of-control programs that threaten the president's budget-reduction goal, the higher-education community sees as a threat to a major part of its financial revenues.

Robert Clodius, head of the National Association of State Universities and Land Grant Colleges, told his members in a memo that "the finger is on the twin buttons of panic and desperation in the area of student aid. Students need the aid to go to school, the institutions need students to sustain operations, and the nation needs trained persons if the economy is to be revitalized and our national defense strengthened."

The lobbying coalition envisions an outpouring of letters and visits to Congress by concerned students, professors and administrators. Clodius' memo said such a response "could have the same impact on the Congress as the thousands of letters that arrived on Capitol Hill in two or three days from Social Security beneficiaries who had heard that benefits would be cut."