Paul Ryan pens an op-ed to defend the Republican budget against the charge that it will harm the poor:

President Obama accused us of wanting to leave children with disabilities to "fend for themselves."
This rhetoric is not just overheated – it is flat-out false. Our budget – "The Path to Prosperity" – strengthens the safety net by directing more assistance to those who need it most. It provides the chronically unemployed with the incentives and tools they need to bounce back into self-sufficient lives.

You can read Ryan's entire column, but -- strangely for a man so prone to boasting of his wonkery and love of numbers -- it contains zero numbers attempting to substantiate his claim that his budget "strengthens," or even fails to shred, the safety net.

If you want actual numbers, you need to go to places like the Center on Budget and Policy Priorities, which lay them out:

Cuts in low-income programs appear likely to account for at least $2.9 trillion — or nearly two-thirds — of this total amount.  The $2.9 trillion includes the following three categories of cuts:
$2.17 trillion in reductions from Medicaid and related health care.   The plan shows Medicaid cuts of $771 billion, plus savings of $1.4 trillion from repealing the health reform law’s Medicaid expansion and its subsidies to help low- and moderate-income people purchase health insurance.
$350 billion in cuts in mandatory programs serving low-income Americans (other than Medicaid).  Chairman Ryan’s budget documents show that he is proposing $719 billion in cuts in mandatory programs other than Medicare, Medicaid, and Social Security, but do not specify how much will be cut from various programs (although they imply that cuts in the Food Stamp Program will be large).   In this analysis, we make the conservative assumption that savings from low-income mandatory programs (other than Medicaid) would be proportionate to their share of spending in this category.  Thus, we derive the $350 billion figure from the fact that about half of mandatory spending other than for Medicare, Medicaid, and Social Security goes for programs for low- and moderate-income individuals and families.  This likely substantially understates the cuts that the plan would make in low-income programs.  The Ryan documents show that $380 billion in cuts would come from mandatory programs in the income security portion of the budget (function 600), and the overwhelming bulk of the mandatory spending in that category goes for low-income programs.  The documents also show $126 billion in mandatory cuts in the education, training, employment, and social services portion of the budget (function 500), which, based on the discussion in those documents, would likely come mainly from cuts in the mandatory portion of the Pell Grant program for low-income students.
$400 billion in cuts in low-income discretionary programs.   The Ryan budget documents released on April 5 showed the plan containing $1.6 trillion in cuts in non-security discretionary programs, but again did not provide details about the size of cuts to specific programs.  (The documents did identify some major low-income program areas, including Pell Grants and low-income housing, as prime targets for cuts.)  Here, too, we make the conservative assumption that low-income programs in this category would bear a proportionate share of the cuts.  Thus, we derive the $400 billion figure from the fact that about a quarter of non-security discretionary spending goes for programs for low- and moderate-income individuals and families.  (Rep. Ryan added $193 billion in cuts in non-security discretionary programs before the budget resolution went to the House floor, but Ryan said these additional cuts would come from freezing federal employees’ pay and reducing the federal workforce, so we do not include them when estimating reductions in programs for low- and moderate-income households.)

I'd deconstruct Ryan's attempt to rebut any of these figures, but he doesn't have one. There's a little bit of hand-waving about turning control over to the states, but he doesn't even try to explain how this would compensate for the massive cuts. Does he think that the federal government is skimming money from the Supplemental Nutrition Assistance Program (formerly food stamps), and that giving states control would somehow overcome the 20% cut? He doesn't say. Does he have an argument that giving states control of Medicaid, which is extraordinarily cheap and has grown much slower than private insurance, would somehow compensate for the trillion dollars in cuts he imposes? No data there, either.

Ryan does, hilariously, argue that he would prevent something terrible happening to funding for the poor:

Mounting debt also threatens our poorest and most vulnerable citizens, because those who depend most on government would be hit hardest by a fiscal crisis. Harsh austerity would be the only course left. A broke government unable to finance its spending commitments would be forced to make indiscriminate cuts affecting current beneficiaries of government programs – without giving them time to prepare or adjust.

The argument is that, if there was a fiscal crisis, it would entail huge and immediate cuts to programs that aid the poor. Therefore we must enact huge, immediate cuts in programs that aid the poor. Oh, and also preserve the Bush tax cuts for top-income earners and cut the rate another ten percentage points. For the sake of the poor.