That number sounds higher than it would effectively be:
1) The population is ~320m, but ~65m of those are under the age of 16 (add on another 8m if you say under 18), who presumably don't need the same $2600/month right from when they are babies. That shaves of $2.8trillion
2) Some people currently on benefits will get to keep all of the $2,600, some people will break even receiving $2,600 and paying an extra $2,600 in tax, and at the richer end of the spectrum they will receive $2,600 and pay more than $2,600 back, to balance it out across society. Even before you start counting the extra money you get from taxing the rich with more than the free income they receive, if you draw a line at the median of society and say that everyone richer than that pays back the $2,600 they receive each month in tax (i.e. saying the richest half don't need this basic income) then that's $3.8trillion that is technically being given out but immediately bein taken back by the Government. (Hopefully they negotiate good bank fees! Obviously the benefit to this seemingly pointless giving out and taking back of money is not having to deal with the legwork of judging who deserves benefits.)
So that's cut almost $10trillion down to ~$3.8trillion that's actually being given out.
3) Now take off current welfare costs. Wikipedia says "Total Social Security and Medicare expenditures in 2013 were $1.3 trillion" and I'm too lazy to find a figure that doesn't include Medicare. Let's imagine that it's split 50/50, we have $3.2trillion left to find.
And this is when you start moving the line we drew down the middle of society and figuring out what % of the $2,600 different levels of society should get to keep or have to pay back in tax or have to pay extra in tax. If you think the rough amount of welfare spent on society currently is right then you can balance it so that less people get supported and less taxes are needed. If you think more people should receive more support and richer people should pay even higher taxes to cover that then it can be pushed in that direction.
The simplest way to logically think "can it be balanced?" is to imagine that 100% of the population gets given $2,600 (or whatever amount) each month, and 100% gets taxed that exact same amount. Everyone is receiving that basic income, and (other than relatively small admin costs) the program is break even. Then you just play with numbers, always balancing both sides, to redistribute wealth from richer people to poorer people (which is already what the welfare system does).