The committee is running ads on Facebook, Google and Twitter urging viewers to click through to a petition to stand against McConnell. It's the first effort in what the DSCC says will be an extended campaign to saddle him with the blame for congressional inaction.

“In three decades as a creature of Washington, Mitch McConnellAddison (Mitch) Mitchell McConnellGOP senator blocking Trump's Intel nominee Spending bill delay raises risk of partial government shutdown support GOP leaders to Trump: Leave Mueller alone MORE has become completely addicted to partisan political gridlock," said Justin Barasky, DSCC national press secretary.

The Web campaign comes as a pro-McConnell super PAC launches television ads targeting Democrat Alison Lundergan Grimes as a "rubber stamp" for President Obama.

Democrats see the Kentucky race as one of a few pickup opportunities in 2014, citing polling that shows McConnell to be unpopular in the state.

McConnell, however, has amassed nearly $10 million for his reelection fight already, and his staff says he's building a presidential-level campaign to support his reelection efforts.