The answer, in short, is yes — very well. A widespread Ebola outbreak here is "not in the cards," the CDC director recently told reporters.
That's partially because the United States has excellent infection control procedures and facilities. Among those facilities is a network of quarantine stations, where the CDC can legally detain anyone who may have been exposed to cholera, diptheria, infectious tuberculosis, plague, smallpox, yellow fever, SARS, new strains of flu, or — relevantly — viral hemmorhagic fevers like Ebola.
Here's a map showing where those quarantine stations are: