Let's see if I can call your bluff here. I'll base this on where I live since it's the easiest.
A quick search shows that rent for a one-bedroom apartment ranges from $550-$700, so I'll go with $600/month for that.
The IRS national standard for food is $325/month for one person.
Utilities. The one-bedroom apartment my wife and I lived in when we first got married was about the same size as the $600/month ones I used earlier, and wasn't far from where I live now. Our utilities came out to around $120/month (mainly because the place wasn't well insulated, as cheap apartments tend to be).
A check of healthcare.gov shows a basic health insurance plan for me would cost $150/month.
Apparel and personal care from the IRS are $122/month.
And 40% of the grocery allowance is $130/month.
The total monthly check I would receive is $1447. That's $17364/year.
The estimated adult population in the US is 242,470,819.
If we assume each of those people only receives $17364/year, that's $4.2 trillion for every adult in America. That's half a trillion more than the entire federal budget for 2014.
And that's probably an underestimate of what it would cost, since I think there are probably more people that live in areas with a higher cost of living than mine than there are in areas with a lower cost of living. Plus I didn't include the increase for being head of household, and healthcare costs rise dramatically as one gets older (I'm 30, if you use someone age 55 for the healthcare cost, it's $300/month instead of $150).
As you pointed out, social security and medicare are $1.3 trillion.
This site lists total state and federal welfare spending, including unemployment, at ~$0.5 trillion. That's only $1.8 trillion. You're still $2.4 trillion short of the low-end estimate of $4.2 trillion I calculated earlier.
In fact, total federal, state, and local government spending for the entire US from the site I linked above is only $6.3 trillion. Your proposal would increase that by close to 70% at least. So explain to me again how there's plenty of money for this suggestion?
No more so than living on minimum wage is now. And I think you underestimate how many lazy people there are out there. I'm sure plenty would be happy to not have to work and live frugally on their government check every month.
As far as fixing welfare, unemployment, and social security goes, there are better ways to do it.
Social Security and Medicare/Medicaid could be fixed quickly and easily by simply raising the age of eligibility.
For welfare, I'd like to see programs that encourage people to work. Instead of just handing out money, give the people jobs doing unskilled labor. And maybe offer people pay matching. For every dollar they make working, they get 50 cents from the government. This would help support people who are working, but are underemployed, and encourage them to work more. And do more to help unemployed people get the skills they need to get a job.