Yes, the Democrats would very much like to see a shutdown

GOP leaders have repeatedly stated their opposition to a government shutdown, and more importantly, their actions have clearly confirmed this position. But Schumer has continued to insist otherwise until only recently. Now he has taken to accusing “extreme elements” within the caucus, namely the Tea Party, of actively pursuing a shutdown to the detriment of a “good and honest man” (Boehner). One Republican source tells National Review Online that it is the Democrats who would like nothing more than to see the government shut down. “It’s practically their only strategy at this point,” the source says. “They refuse to cut spending and they think a shutdown would benefit them politically by turning the public against Republicans.”…

“Unfortunately, [Schumer and Dean’s] comments are not surprising,” says Michael Needham, CEO of Heritage Action. “The defenders of big government have made perfectly clear they have no intent to cut spending and get our country on the path to prosperity. Rather, their focus is on denigrating conservatives and reelecting President Obama in 2012.”