Just for posterity, to help future fellow Googlers, I'd like to expand on EMP's answer.
EMP's answer provides the time in UTC (if that's what you're looking for, use that).
To arrive at the client local time in C#:
In JavaScript:
var now = new Date();
var UTC = now.getTime();
var localOffset = (-1) * now.getTimezoneOffset() * 60000;
var currentTime = Math.round(new Date(UTC + localOffset).getTime());
In C#:
DateTime currentTimeDotNet = new DateTime(1970, 1, 1).AddTicks(Convert.ToInt64(currentTime) * 10000);
Credit to this blog and EMP's answer, but took some trial and error on both ends to get it right, so just fyi for future folks.