Fox News' Sean Hannity Told Republicans To “Hold The Line” On Shutdown. On October 1, the first day of the government shutdown, Fox News host Sean Hannity took to his radio show, The Sean Hannity Show, and encouraged Republicans to continue the shutdown until their demands are met:  

HANNITY: My advice to the Republicans: Hold the line. Stand on your principals. Stand with the American people. Stand for the best healthcare system. [Premiere Radio Networks, The Sean Hannity Show, 10/1/13]

Hannity: “Worst Outcome” Is For Republicans “To Cave” On Ending Shutdown. Later, on Fox News' Hannity, host Hannity told Sen. Rand Paul (R-KY) that he didn't think Republicans “should give in at all” to demands to end the shutdown:

HANNITY: I think the worst outcome, though, for the Republicans in the House at this point -- as they have been reasonable and the president totally unreasonable, Reid unreasonable -- is to cave. I don't think they should give in at all. And if that means that they're going to sit this out for a month or two months, or however long the president wants to be arrogant and not talk to anybody, then just sit it out. [Fox News, Hannity, 10/1/13] 

Dana Loesch: Republicans Should “Finish The Race, Stay On Course” On Shutdown. When Rep. Scott Rigell (R-VA) tweeted in favor of passing a continuing resolution that would fund the government without changing any other policy, conservative radio host Dana Loesch replied that Republicans should “finish the race” on the shutdown over the Affordable Care Act: 

[Twitter.com, 10/1/13] 

Later, Loesch tweeted that she agreed with Republican lawmakers who were cheering the shutdown of the Environmental Protection Agency (EPA) as a result of the budget impasse:

[Twitter.com, 10/1/13]

Breitbart.com's John Nolte: “Hang In There, GOP!” Breitbart.com columnist John Nolte reacted to the government shutdown by encouraging Republicans to “hang in there” and not negotiate with Democrats:

[Twitter.com, 10/1/13]

Fox News Radio's Todd Starnes: “It's Not A Good Fight If You Surrender.” Responding to Rep. Scott Rigell's (R-VA) call for Republicans to negotiate with Democrats, Fox News Radio host Todd Starnes encouraged Republicans not to surrender on the shutdown: 

[Twitter.com, 10/1/13]

Fox News' Erick Erickson: “House Republicans Should Hold The Line On Shutdown.” In an October 1 FoxNews.com piece titled “Republicans, stand and fight or risk getting nothing from government shutdown,” Fox News contributor Erick Erickson wrote (emphasis added):

House Republicans should hold the line. They should demand that ObamaCare be defunded. They are going to get the blame for a shutdown. They might as well own it and keep it shut down until they get their way.  

Sure, it will take time, but eventually Barack Obama will blink. I do not think, despite what fickle polling says, that the Republicans will be blamed by killing ObamaCare.

[...]

This is a winning issue for the Republicans if they just have the will to fight.  But too many of their old guard and outside pundits have been wringing their hands over this for a month.  They have not wanted to fight and preemptively took all the blame. [Fox News.com, 10/1/13]

Fox News Contributor Laura Ingraham: Federal Employees Going Without Pay Is “A Dream For A Conservative.” On The Laura Ingraham Show, host and Fox News contributor Laura Ingraham said furloughs for nonessential government workers due to the shutdown were “a dream”: 

INGRAHAM: I slept so well last night. I felt, I don't know, an extra spring in my step. Maybe it's just I feel somehow things are lighter today. The air is crisper, clearer, cleaner. Because we have a lot of nonessential federal employees not being paid. See that's a dream for a conservative. When nonessential federal employees are not clogging up our roads and being paid with my tax dollars. [Courtside Entertainment Group, The Laura Ingraham Show, 10/1/13]

Fox News Contributor Sarah Palin: Caving On The Shutdown “Would Be The Worst Case Scenario” For Republicans. During the September 30 edition of Fox News' Hannity, Fox contributor Sarah Palin urged Republicans not to cave in to demands to prevent the looming government shutdown:  

HANNITY: What do you think the worst case scenario for the Republicans is here?

PALIN: Yeah, it would be to cave. That would be the worst case scenario. And this will impact the 2014 midterm elections. [Fox News, Hannity, 9/30/13]

CNN Host Newt Gingrich Tells Republicans “Don't Cave On Shutdown.” In a September 30 opinion piece on CNN.com, former Fox News contributor and current CNN Crossfire host Newt Gingrich wrote that House Republicans caving on the government shutdown would be the “worst possible outcome for the country”:

The worst possible outcome for the country from the impasse over the continuing resolution that would prevent a government shutdown would be for House Republicans to cave.

[...]

Any surrender on the continuing resolution would confirm the contempt with which Obama and Reid already hold Boehner and his Republican colleagues. This fight is about something much bigger than the Republican Party and the future of Obamacare.

[...]

The next few weeks might be painful if House Republicans insist on getting to a compromise and refuse to surrender. But the next three years will be frightening if House Republicans cave and the president learns that nothing stands between him and his ability to use overweening power outside the Constitution to advance his ideology.

This is a big moment of decision for America. Don't give in now. [CNN, 9/30/13]