"We are still in charge until Jan. 20 and are still responsible for making decisions of the government," President Reagan reminded his Cabinet last week.

But there really isn't much in the way of serious problem-solving that Reagan and his administration can accomplish in his final 10 weeks in power.In fact, some of the burdens Vice President George Bush will inherit from Reagan seem to be growing heavier day by day.

Foremost among these is the federal budget deficit. Three months ago, the federal deficit for fiscal year l990, which begins next Oct. 1, was projected to be in the range of $111 billion. More recent calculations have pushed the deficit much higher, in the range of $130 to 140 billion.

But under the Gramm-Rudman-Hollings balanced budget law, the 1990 deficit must be held to $100 billion, or deep cuts in both defense and domestic programs are triggered automatically.

The proposed FY 1990 budget will be submitted to Congress on Jan. 9. It will be Reagan's last budget, and like many that preceded it, this one is sure to be pronounced "dead on arrival."

It will then be up to Bush, who will take office on Jan. 20, to thrash out a compromise with the Democratic Congress.

Having pledged no tax increases, it is difficult to imagine how Bush will be able squeeze $30 to $40 billion in savings out of the 1990 budget and still deliver on his campaign promises to protect the defense and boost outlays for education, child care, health care and anti-drug programs.

Nor is there any sign that Reagan can make any further substantial progress in nuclear arms control talks with the Soviet Union. The current round of talks in Geneva on strategic weapons is due to end in mid-November.

In the Middle East, a hardening Arab position in response to the recent Israeli elections is already manifesting itself in renewed West Bank violence and escalating PLO political demands.

In Central America, the defiant Sandinista government of Nicaragua continues to enjoy strong Soviet and Cuban support as the U.S.-backed Contra rebels languish.

Nor is Reagan expected to find a solution to his stalemate with Panamanian strongman Manuel Noriega.

So there will be no shortage of problems awaiting President Bush, but there is a great mystery about how he will attack them. At the moment, Reagan's vice president is concentrating on preparing for a smooth transition of power.

Indeed, the way Bush handles the transition will be an important signal about the kind of administration he will run, according to many political experts, including Robert Strauss, a former Democratic national chairman greatly respected by leaders in both parties.

The two best transitions Strauss says he can recall were the ones run by Republican Richard Nixon and Democrat John F. Kennedy.

Why?

"Because both Nixon and Kennedy understood government," Strauss says. "Nixon knew the kind of government he wanted to put in place. He knew the kind of issues he wanted to handle himself, and those he wanted handled by others."

Similarly, Kennedy's transition was successful because he picked "a very, very strong person to head it, a fellow who knew government. He picked Clark Clifford, who'd been deeply involved for years, who knew what it took, had experience, understood Washington," Strauss says.

Democratic President Jimmy Carter and Republican Ronald Reagan presided over "poor" transitions because they relied upon aides who lacked the "backgrounds and skills and knowledge of what makes Washington work."

Strauss made those comments early on Election Day before the outcome was known. But if Bush were elected, Strauss said he was confident he would establish a good transition team, with the help of his campaign chairman James A. Baker III, who Bush has since designated to be his secretary of state.

"George Bush has certainly been in town a long time," Strauss said. "He knows what it takes. He knows how a transition should function. My judgment is he and Jim Baker understand that better than most."