I encountered the same problem at appx. 7:30 pm ET today (4/10/18).  It appears to be a temporary problem with the Intuit site.You may choose to file your federal return now - if you haven't already - and come back later and file your state return.

From my experience I was able to update my credit card by confirming it first then hitting continue. If you had already confirmed the card info then as a computer technician I would tell you some browsers may not support the continue button. Change your default browser to Edge or Internet Explorer at least temporarily and try again. I at first tried firefox without success then IE still no good then I tried Edge and for some reason that worked. I have not tried Chrome as I did not have it at the time.