If the question is whether I think the government should issue paychecks to guardians who stay home to raise children solely because they choose to stay home to raise children and manage a household, then my answer is no.
Don't get me wrong. I think the work is difficult, and it deserves actual compensation, including a retirement plan, a disability policy, some vacation time, sick days, medical and dental coverage. (But maybe I just think that we all deserve those things - regardless of employment status.)
As a policy issue, and not a personal one, I think we all recognize that reproduction is a necessary function of a healthy society. On the other hand, as a society, we want and need able-bodied adults to join the workforce and to be productive. In the absence of consensus about the benefits for kids (and society) of having two working parents/guardians, governmental guarantees for paid parental leave from work seem to me like the best solution.
And it is worth noting that the U.S. is the only industrialized nation that fails to provide its parents with any guaranteed paid leave after the birth or arrival of a child. If you are interested in checking on the rest of the world, follow this link: http://www.npr.org/2011/08/09/137062676/time-with-a-newborn-maternity-leave-policies-around-the-world.