The Reagan administration's plan to make drastic new cuts in the government's $6 billion program of financial aid to college students already is running into opposition in Congress.

About half the nation's 12 million college students are getting some federal financial aid this year. Sen. Robert T. Stafford (R-Vt.), chairman of the Senate Labor and Human Resources subcommittee on education, said yesterday that he doesn't believe his colleagues will approve proposals that would cut millions of grant and loan recipients. "This is what you might call the educational safety net," he said. "We've cut as far as we can."

Rep. Paul Simon (D-Ill.), chairman of the parallel House subcommittee, agreed. He noted that blue-collar workers in his Illinois district already are asking about the budget's effects on college aid. "I cannot believe that Congress will go along this time," he said.

In outlining the Education Department's budget in a briefing for reporters Saturday, Secretary Terrel H. Bell noted that the spiraling guaranteed student loan program has been consuming the federal education dollar; in fact, the administration will have to send Congress a $1 billion supplemental appropriation request this fiscal year for the program. In 1977, the program cost the government $367 million; in fiscal 1983 it will cost $3.4 billion unless Congress makes the changes the administration proposes, he said.

Under the proposed changes, designed to save $900 million:

All applicants would have to undergo a "needs" test. Now, only families with incomes of more than $30,000 a year have to pass a needs test.

The loan "origination fee" would be doubled to 10 percent. That means, for example, that a student has to borrow $2,200 to get $2,000.

Borrowers would have to pay market interest rates two years after leaving school rather than the 9 percent they pay now.

Graduate students would be cut out of the program and would have to borrow at 14 percent rates under a new auxiliary loan program that is not available in all states. About half the nation's 1.2 million graduate students now have guaranteed loans.

The administration has requested that the changes be approved by April 1, so they can be used to hold down the cost of the guaranteed student loan program for the next school year. Stafford and Simon both said they see little chance of any action that quickly.

This school year, 3.5 million students have $7.7 billion in guaranteed loans. The program's outstanding loans now total more than $18 billion and are expected to rise to $32.5 billion by 1983, according to department estimates.

The government pays the student's 9 percent interest rate while he or she is in school and pays the bank the difference between that rate and current market rate until the loan is repaid. The interest subsidies and loans that have been written off are expected to cost the government about $2.5 billion in this school year.

Guaranteed student loans and the other main federal college assistance program, the so-called Pell grants for needy students, have grown rapidly since Congress passed the Middle Income Student Assistance Act in 1978 to head off a drive for tuition tax credits.

Pell grants now go to about 2.7 million students and cost $2.3 billion. The administration proposes to lop nearly 1 million students off the rolls and reduce the funding to $1.4 billion. It also proposes big reductions in the $1 billion campus-based programs, cutting work-study substantially and eliminating two other programs.

Education officials said in the budget briefing that the administration has retargeted the Pell grant money so most of it goes to the poor. Under current rules, a student from a family of four with an income of about $27,000 a year is eligible for a small grant. The new budget contemplates cutting the income level to $18,000.

The nation's colleges have started an ambitious grass-roots lobbying effort to stop the cuts. They have blanketed their member schools with dire warnings about the proposed cuts in the hopes of having Congress flooded with protests from students, parents, professors and administrators.

Charles B. Saunders Jr., chief lobbyist for the umbrella American Council on Education, said yesterday that the response from Congress is encouraging so far. "Last year they told us, 'We have to give the president the bottom line.' This year they're telling us they'll fight all further cuts in student aid."

If the president gets his way, Saunders said, the cuts will change the face of American higher education. Some small liberal arts colleges will fold. Because of the costs, students will have to turn to public schools that are cutting enrollments because of declines in state aid. Elite colleges will become the home of the wealthy only, he predicted.

Over the weekend, for instance, the board of trustees at exclusive Wesleyan University in Middletown, Conn., ended a decade-long policy of accepting students without regard to their financial needs. Each of the school's 2,600 students faces an $11,000-a-year bill for college education.

While administrators claimed the school still will recruit minorities, some students protested that the policy would eliminate the middle-class student who wouldn't have access to as much financial aid under the Reagan administration's proposed cuts.