It appears that the Texas Health Presbyterian Hospital Dallas, where a 2nd worker has now tested positive for Ebola, initially lacked proper equipment and training. From The Washington Post:
The CDC’s Rollin, who spent nearly three months in West Africa fighting the Ebola outbreak, and who has studied Ebola for three decades, flew to Dallas on Sunday and held intensive discussions with doctors and nurses at the hospital about how they had handled the Duncan case.
He said the hospital originally had no full-body biohazard suits equipped with respirators but now has about a dozen. Protocols evolved at the hospital while Duncan was being treated, he said: “Collecting samples, with needles, then you have to have two people, one to watch. I think when the patient arrived they didn’t have someone to watch.”
Dallas hospital learned its Ebola protocols while struggling to save mortally ill patient - The Washington Post