I can agree with the points made in these videos - although they were extremely romanticized. Most people who are educated on the progressive benefits of NASA programs will not disagree that the lack of funding is a hinderance to the long-term advancement of society; however, NASA is absolutely not the "great bastion" of technology. American (scientific) achievements are not dependent on the program's funding.
With NASA receiving ~1% of the federal budget (reference), we have seen the creation of Apple and Windows software (1984-85), cellular telephones (1988), Doppler RADAR (1988), 3-demensional graphics and high-definition screens (late 1980's - 1990), HTTP & HTML (1990), DVD (1995); plus nano-technlogy, birth control, energy alternatives, hybrid vehicles, the internet explosion, and countless discoveries and breakthroughs in the scientific field including medicine, geology, physics, and yes even astronomy (2000 - current). The resounding argument from the videos seemed to be strictly environmental. In fact, NASA has benefitted from advancements that they had no part in. Technology is growing at an exponential rate despite the unfortunate situation.
Tyson made a great observation for why our "attention" is being turned away from space temporarily. Quite simply, we have no real competition or motivation. The primary cause of the space race was fear. America has a passion for staying on top. Thus, with no challenger, it seems like a waste to dedicate energy to a program that - while not useless - is unnecessary. (Though we may see a miniature space race in the near future).
Furthermore, the American programs which are agreeably a waste of money and/or do not work in their present forms are not direct reasons to designate their funding to NASA. Most of the programs in question were intended to better society in education, security, and health. Would you disagree that these aspects of our culture are important? We should not give up on improving conditions simply because current solutions have complications - however large or small. Before we can spend money on space exploration (which is, at the moment, not a pressing matter), we must first train and educate the future astronauts, scientists, and perhaps inter-planetary colonists. Before we can safely venture to other celestial bodies, we must first have a home secure from foreign threats in addition to threats within our borders. Before we can live on Mars, we must be able to live on Earth.
The War on Terror has obviously been a heinous misallocation of resources (especially human). Iraq was a total failure of intel, and the response to the terrorist attacks of 9/11 was grossly exaggerated. And, the irresponsible attempt at nation-building in the Afghan region is done in vain. However, like with all federal programs/operations, the method is the key factor in determining if an endeavor is worth the cost. American "diplomacy" was abysmal under the Bush administration, yet it shows signs of improving in the future despite the Iran nuclear controversy. What is clear is that we should be devoting our energy to ensuring the safety and well-being of American citizens (in addition to human rights all over the world). We must first be able to work together in remote harmony before investing in an unnecessary program.
Some good news for space/NASA enthusiasts is the growth of private space organizations. The CRS-1 mission of last year is proof that we do not need to fund NASA in order to continue our research and exploration of outer space. I would even venture to say that by allowing non-federal projects we will see more advancements than with NASA exclusively. While I am not suggesting that increasing NASA funding to 1% would be wasteful spending, it is clear that the fanciful international space race can be put on hold for the time being; and, the federal budget can be put to better use (ie: improving social programs).
In summary, I agree that the United States has wasted a substantial amount of money on global and internal affairs. Thus, I would have to agree that the money wasted could have given NASA a plethora of opportunities in space exploration and colonization. However, due to our present situation, we should focus more on the betterment of our educational and health systems in addition to the tension brewing in the Middle East. For the time being, research should be left to private organizations such as SpaceX. But, through the social program improvement process, we may find that money no longer needs to be given in such large quantities to the currently problematic solvents after they are "fixed". That money left over can then be designated back to NASA under the assumption that we do not see an economic collapse or significant global conflict.