I was their first known call from the website. While Rep. Rokita has been getting calls about the shutdown, "This site is news to me," said the woman answering his phone (she did confirm my number was obscured). When asked if any drunk dialers had called at all, like, people who were really drunk, she replied, "No."
Not yet at least.
The website was created by Revolution Messaging, which helps organizations spread messaging through mobile texts or calls.
"We were discussing how members of the House were supposedly drinking during the votes being cast the night before the shutdown, and also we had friends who were furloughed and taking advantage of specials at bars," said Revolution Messaging's Keegan Goudiss. "We thought this would be a great way to spend their time drinking during the day—calling random members of Congress and telling them to resolve the shutdown."
(Read more: How 'preppers' are gearing up for a US default)
In the first four hours after the site went live, Goudiss said they processed 2,000 calls.They aren't making money on the venture, but it's highlighting their technology and getting attention. The voice on the recorded call I received was staffer Rich Ranallo.
"He was sober for the taping of the message, but plays a surprisingly good drunk," said Goudiss.
Drunk Dial Congress even has drink recipes, in case you actually intend to put the drunk in drunk dialing—responsibly, of course. You can brace yourself with "The Bad Representative," a cocktail of whiskey, cherry brandy, lemon juice and vermouth. Or "The Sleepy Senator" made of absinthe.
"Someone called us and asked why we don't have any beer recipes on the site," said Goudiss. "We just discussed adding a beer shandy."
Drink, dial and rant all you want, but if we really want this impasse to pass, maybe we should ban members of Congress from drinking any alcohol until the shutdown ends. The government would open for business tomorrow.
—By CNBC's Jane Wells. Follow her on Twitter: @janewells