I […] can't help wondering why USA […] can not manufacture this chemical themselves.
They can and they did!
Back in the nineteen thirties, Ernest H. Volwiler and Donalee L. Tabern filed a couple of patents on sedative thiobarbituric acid derivatives for the Illinois-based Abbott Laboratories. Among these was US 2,153,731 for sodium thiopental.
Abbott Laboratories produced it for a long time and when the company was restructured, the still Illinois-based split-off Hospira continued the production.
Note that it is not a "bad compound" as such and actually, it is still listed as an alternative to propofol on the WHO Model List of Essential Medicines.
According to a 2010 article in the German ÄrzteZeitung (online, 29.09.2010), the FDA was aware of the thiopental shortage and a speaker of Hospira told the NYT that his company is rather unlucky about the fact that this anaestetic found it's way into death row.
Around this time, the production of thiopental at the facilities in Illinois was seemingly stopped.
In a 2011 article in the ÄrzteZeitung (online, 24.01.2011) it is stated that Hospira had initially announced to continue the production at a facility in North Carolina and in Liscate, Italy.
However, it seems that the production in North Carolina never started. Moreover, the Italian authorities demanded a declaration that the thiopental produced in Liscate would not be used for lethal injections. Obviously, Hospira could not comply.
Personally, I think that Hospira wasn't overly unlucky about the legal situation in Europe. They are a health care company and I suppose that they prefer to make profit by improving the medical situation of their customers, rather than by killing them!