How much it costs to provide $30,000 to each and every US resident can be computed with a simple multiplication. For 320 million people, it works out to 9.6 trillion dollars. If we restrict the program to adults over the age of 20 and to the $11,670 poverty threshold from the Department of Health and Human Services for a single-person household, we end up with $2.7 trillion (all numbers for 2014 or 2015, source: Wikipedia articles on Demographics of the United States and Poverty in the United States). Those are obviously very rough estimates but it's useful to seriously consider these numbers to get a feeling of the magnitude of the costs involved.
On one level, it's not absurdly high. After all, US GDP per capita is a little more than $53,000 so the country does produce enough to give everyone $30,000 per year. Beyond that, determining what it would mean for the economy is obviously a very complex question and would require some assumptions and probably a bit of modeling that's way over my head.
But that's not really the point of the argument. The point is that $9.6 trillion is way more than the cost of current welfare programs, total discretionary spending or even the total amount of taxes collected at all levels of government in the US. Even the lowest $2.7 trillion estimate is close to the entire federal budget ($3.6 trillion in 2013). Finding that much money would require giving up every existing program, disbanding the military, drastically increasing taxes and fundamentally upsetting the way government works in this country.
Just to give an example, SNAP benefits (food stamps) cost only $76.4 billion in 2013 or 0.8% of the $9.6 trillion we need. It's the first thing you listed because it's the first thing that comes to mind when thinking about welfare but it's actually really small relative to the population, the size of the economy or the federal budget. The total cost of all means-tested programs was only $927 billion in 2011, 9.7% of our high estimate and 34% of the low estimate (and that number includes Medicaid, more on that below).
If we assume this basic income would be paid to all adults and could therefore replace Social Security, we can also add that money ($785 million in 2011) to the pot but it's still not enough. Note that you frequently hear people warning that the cost of all this has increased and is or will soon become unsustainable but most of the time, the figures include social security and Medicare.
It's relevant because if we consider that funding a basic income scheme would require all the money currently going towards means-tested programs and programs helping the elderly, it would also mean stopping Medicare and Medicaid. All the current beneficiaries would therefore need to pay for health insurance out of pocket, which would in turn imply a large cut in their disposable income. For a given level of funding, it's a massive transfer from those currently benefiting from various welfare programs to those who are above the thresholds (for whom the basic income is a kind of cash allowance on top of what they already get).
Looking at it from another angle, $9.6 trillion is about 57% of GDP which is more-or-less the level of government spending in France or Denmark, the (stable/developed) countries with the highest level of government spending in the world. That's the entire government spending, which include things like law enforcement, military spending, investments in infrastructure, debt service, etc. and, for these countries, education and healthcare. All this would still need to be funded somehow.
An argument you sometimes hear from proponents of a basic guaranteed income is that current welfare programs waste a lot of money because the constant suspicion that recipients are lazy “moochers” leads to increasingly arcane, arbitrary and intrusive eligibility requirements and huge administrative costs to handle them and fight fraud. If we establish that everybody is entitled to a basic income, we just need to ensure each person is paid only once and we can do away with most of the administrative overhead and the whole debate about what's fair or not.
It's an intriguing idea but the simple calculations I just presented show that the numbers do not add up, we still need a lot more money than what's already available for social programs. Importantly, some of the people who make this argument that a (meaningful) basic guaranteed income would cost too much are left-leaning economists who are sympathetic towards the welfare state. It's not simply the welfare-is-too-high-we-can't-afford-to-pay-for-anything line of those who favor tax cuts no matter what.
You could still make an argument for basic income based on some optimistic view of its effects on the society (e.g. arguing it will boost demand, free up people to be more innovative, educate themselves without going in debt, reduce the massive costs created by poverty, etc.) but it's quite clear that you cannot fund it at this level using the money currently available for welfare programs or get anywhere close to that in the current political context.
Even in European countries with large welfare states and less ideological prevention against government intervention in the economy, it sounds more like a pipe dream than a serious policy proposal…
ADDENDUM: In a completely different context (namely the UK), here is another attempt at putting a specific cost on a basic income scheme (from people who are favorable to it). Based on a similar multiplication, they arrive at a total cost of GBP 276 billion and then explain how to pay for it.
The main difference with the proposal discussed above is that this citizen's income would be GBP 71 per week for an adult, well shy of the UK's poverty line. (Note however that poverty is defined and measured differently in Europe and that it make most sense to look at households rather than individual persons). It can be valuable nonetheless but it's a very different idea.