Nearly five months after the shuttle Challenger was destroyed and two weeks after the Rogers commission issued its findings, the U.S. space program is still a Humpty Dumpty that Washington policy-makers don't know how to put back together.

It's not just that they can't agree. Part of the problem is that there are few good choices.

President Reagan's moving declarations of commitment to the space program contrast starkly with his administration's indecision over the question of whether to build a replacement for Challenger, and if so, what kind, over what time period and how the multibillion dollar craft should be financed in the era of Gramm-Rudman-Hollings budget restrictions -- another of Reagan's passions.

Congress has flailed through hearings rehashing the presidential commission's thorough investigation into important but relatively narrow questions of what caused the accident and how the National Aeronautics and Space Administration can avoid another.

Members of Congress have expressed both guilt, that they long allowed so much to slip by them in their oversight of the space agency, and resentment, that NASA officials misled them badly for over a decade about how "routinely" and "cheaply" the shuttle could operate. Many have promised a closer scrutiny of NASA.

In the past, hearings focusing broadly on the future of the space program have attracted few headlines. Perhaps mindful of this, several members have made a show of calling for specific heads at NASA to roll -- most of them already chopped in the career sense. Sen. Ernest F. Hollings (D-S.C.) accused one NASA official of willful "gross negligence" in allowing the launch of Challenger.

But this kind of sound and fury does not address the tough calls that must be made in the next few months:

In the view of many, the question of Challenger's replacement should be part of a much broader reassessment of the civilian space program. But some administration officials, members of Congress and others are concerned that this fundamental review is not being done.

Rather, the fourth orbiter has become an emotional symbol of support for the space program, the purveyor of a "quick fix," and all other actions wait upon this decision.

John Logsdon, a space expert at George Washington University, noted that "by coincidence, we have the accident to dramatize the poverty of the current space policy; the Paine report the wide-ranging recent report of a presidential space commission ; the Rogers report; and new leadership at NASA, all at the same time.".

"If we can't go back to basics and have a realistic debate now," he said, "we're never going to do it."

"This is exactly the right time for a full-blown and wide-ranging debate about the purpose, focus and scale of the American space program," said Sen. Albert Gore Jr. (D-Tenn.), who sits on a Senate committee that oversees NASA. "Many of the problems that have occurred since the Apollo program might have been avoided if there had been clear answers to these kinds of questions."

The fireball that destroyed Challenger also burned away what was passing as the rationale for the shuttle program -- that it could fill all the nation's scientific, military and commercial space transport needs -- and eventually fly routinely and cheaply enough to pay for itself. An essential part of that promise was that it would make the old-style "throw-away" rockets obsolete.

Now the Pentagon, along with at least one top NASA official and independent scientific experts have endorsed moving as much shuttle cargo as possible onto unmanned throw-away rockets, reserving the shuttle for payloads that require humans, such as scientific experiments and satellite repairs.

This would mean, among other things, that hundreds of millions of dollars in revenue from paying shuttle clients would be lost to NASA, and extra billions would be required to build and maintain dual manned and unmanned launch systems. Some also think that it would also give life to the commercial unmanned launch industry, held back until now by NASA's subsidized shuttle.

"The question that has got to be raised in our hearings is what is our space policy, now that one of the fundamental assumptions in it has been proved wrong," said an aide to the Senate Appropriations subcommittee that funds NASA.

And decision-makers must come to grips with the notion that the country can't have the champagne space program it has come to expect on the beer budgets it is providing.

The estimated $3 billion bill for a new orbiter would amount to nearly half of NASA's annual budget. The money has to come out of NASA's pocket or from other government programs, White House budget-watchers say.

The shuttle is already considered "old" technology, and some experts are arguing for building an advanced replacement for Challenger. But this would take much longer. Reagan has already told NASA to study an "Orient Express" space plane that could fly into orbit from ordinary airports.

The president also has endorsed the construction by 1992 of a space station as the shuttle's intended destination and the "logical next step" in NASA's blueprint. It would cost an estimated $8 billion. NASA Administrator James C. Fletcher has said that, if he had to chose between a fourth orbiter and a space station, he would choose the latter -- but its supporters are nervous.

Meanwhile, NASA's space science research programs have languished, and saving them will cost more megabucks. For example, with NASA's cancellation last week of its Centaur booster program on grounds that it was not safe enough, the planetary probes that were to be boosted from the shuttle into deep space to study Jupiter and the sun may be switched to unmanned launchers. The estimated cost of such a move is over $1 billion.

All this is in addition to the still-mounting costs of recovering from the Challenger accident, not to mention the kind of soul-gripping goal some are pushing for, such as a U.S.-Soviet manned mission to Mars.

Much of the debate inside the administration centers around "stretching out" the pace of building and funding a replacement orbiter and/or the space station.

"Something's got to give," said a House science and technology subcommittee aide who specializes in space issues.

Whatever public debate there is will not begin in earnest until the administration finally, as the aide put it, "sets up a straw man" -- a recommendation with a dollar figure -- for everybody to shoot at.