The site, built by Google sister-company Verily, is supposed to offer people who live in San Mateo or Santa Clara counties and think they are experiencing COVID-19 symptoms a way to schedule a test. Verily built the "Project Baseline" site in tandem with the California governor's office and other local, state and federal officials.

President Trump announced the site on Friday , which was reportedly before Alphabet was ready to go public with the launch, and got some details about the site wrong.

Alphabet' s Verily coronavirus site screening website for Silicon Valley residents went live on Sunday evening . By Monday morning it appeared to be overloaded and cannot currently offer appointments for screenings, according to the website.

The site says you should seek out professional medical attention if you're experiencing "severe cough, shortness of breath, fever, or other concerning symptoms." But, if you don't have those symptoms but are worried and want a test, you can proceed to try to schedule a screening. However, instead of offering one, the site now says:

"Unfortunately we are unable to schedule more appointments at this time. Appointments will continue to expand through this program as we scale capacity in the near future. Please check back later. In the meantime, we recommend following these guidelines from the CDC. You can read more about the Baseline COVID-19 Program here."

"All appointments require a call-back confirmation to schedule an appointment," a Verily spokesperson told CNBC. "If someone were to fill out the questionnaire overnight, they would go into a queue to be called the next day should they qualify. In these first few days of this pilot, we expect appointment availability to be limited as we stand up operations and that testing capacity will increase in the days to come."