We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.
The Constitution tells us what the government is supposed to do. How does the space program fit in? For the most part, to '... promote the general Welfare,' in other words, to benefit most Americans. To a certain extent NASA's current program does that, but a lot of the money spent only benefits a small slice of American society. What would a program focused solely on promoting the general welfare look like? Here's my take on the priority order:
Unfortunately, NASA has a terrible record of developing low cost launch vehicles. The shuttle was supposed to be $500/lb to orbit but actually costs over $10,000/lb. Several subsequent projects failed to get anything into space at all. NASA does do a good job of research, and could develop radical new technology like electromagnetic first stages, aerospike nozzles, air-breathing hypersonic propulsion, space elevators and so forth; but the key is high launch rate. Today there are only 50-100 launches a year, too few to generate economies of scale. We need to support commercial markets that require high launch rates, at least thousands per year. That means supporting space tourism, the only market for high-volume human launch, and space-based solar power (see below). See Contest-Driven Development of Orbital Tourist Vehicles" for data on the tourist market.
Also not on the list is ISRU -- in situ resource utilization -- a fancy term for mining off planet. However, finding and deflecting NEOs is a good first step towards mining them; and very large scale SBSP is probably best done with lunar materials. Consider, to provide all the energy used on Earth today would require perhaps 30 million tons of solar power satellites in orbit. Most of that mass is silicon and metal, both of which are available in ample supply on the Moon. It requires a lot less energy to get materials from the Moon to typical SBSP orbits than from Earth.
Also not on the list is the 'human space program.' That's because putting small numbers of astronauts in space has done little or nothing to directly benefit most people, although spin-off technologies have been valuable. However, there are a number of companies planning to offer tourist rides into space in the next few years. One, Virgin Galactic, is planning 40 vehicles each capable of carrying six people into sub-orbital space twice a day. Furthermore, Bigelow Aerospace, which has flown two subscale space stations, is negotiating right now with major aerospace companies for twelve flights a year to put up a space station and fly astronauts to it. This is a far higher flight rate than the U.S., China or Russia has ever achieved in their manned program. Human space flight may be best left to the private sector.
There you have it, a space program for the people. This program isn't driven by national prestige, curiosity or altruism. It does what the federal government is constitutionally required to do: "... promote the general Welfare."