Miller, who is in a tight contest with the incumbent Alaska Senator Lisa Murkowski following Tuesday's Republican primary, currently holds a narrow lead as absentee ballots are being counted.
Appearing on CBS' "Face the Nation," Rep. Debbie Wasserman Schultz, D-Fla., described the GOP primaries, and yesterday's rally in Washington led by conservative commentator Glenn Beck, as a sign that "There is a raging battle going on within the Republican Party for the heart and soul of the Republican Party."
Speaking of Tuesday's primary battle in Alaska, which follows Utah Republicans' choosing a Tea Party-backed candidate over an incumbent Senator, she said it was "hard to know where the Republican Party ends and the Tea Party begins. They've struggled to elect, and actually have not been able to successfully elect, their moderate candidates, the mainstream candidates. The Tea Party candidates seem to be winning because the Tea Party Republicans are energized in their primaries.
"I think a pretty difficult problem for them going into the November elections because they have candidates like Miller who are on the extreme right wing fringe who want to end Medicare as we know it, yank the safety net out from under our senior citizens. I mean, Americans are really going to have a very clear choice set up in November, between moderate Democrats who are centrist, where the country is, and Republicans who are really off on the right wing fringe."
Miss. Gov. Haley Barbour, also appearing on the program, dismissed Wasserman Schultz's suggestion that Republican incumbents fear a Tea Party insurgency.
As a past chairman of the Republican National Committee and current chairman of the Republican Governors Association, Barbour said, "We never took sides in primaries. We did not endorse incumbents over challengers.
"Here's why: The Republicans of Alaska have the right and should pick their nominee. They don't need somebody in Mississippi to tell them who ought to be the Senator of Alaska."
Schieffer asked Barbour if in November the GOP would have a hard time selling Miller and other far-right candidates (such as Rand Paul in Kentucky, who said restaurants should be permitted to discriminate against customers based on race, and Joe Buck in Colorado, who warned building bike paths would make Denver subservient to the United Nations). "It seems to me you do have an exotic crew out there this time," Schieffer said.
Barbour instead suggested that the success of far-right candidates was a response to the Democrats making what he termed "the biggest lurch to the left in policy in American history.
"No Congress, no administration . . . has run this far to the left in such a small period of time," he said. "There is a reaction to that. Those hundreds of thousands or hundred thousand, however many there were on the mall yesterday, were reacting to that. They're very concerned about where our country is being driven by the Democratic majority.
"As far as talking about less money [from Washington], look, my budget this year in Mississippi is 13% less than it was two years ago. I cut spending 9.7% last year. Frankly, nobody much noticed the difference. We were able to continue to provide services. People weren't kicked off Medicaid," Barbour said. "The fact is, the country is going to have to spend less money. If Joe miller was trying to say that in a different way, he is right if what he's saying is our country has got to spend less money. We're been on a spending spree that made drunken sailors have a bad name."
Wasserman Schultz said that the overriding concern of voters will be the economy, which she said has been showing signs of slow improvement. She believes Americans do not want a return to the Bush administration policies that boosted the nation's deficit spending.
"The American people are going to make a choice in November between right wing extreme Republican candidates who want to take us back to where we were when President Bush was in office, backslide toward the Bush era, change Social Security to a privatized program that invests the money in the stock market - where would we have been if we had done that in the last few years? Voucherize Medicare and essentially change our tax policies to one that is again focused on the wealthiest 2% of Americans?"
She also argued against Barbour's take on Democratic policies. "We gave 95% of Americans a tax cut, so I don't know how giving the overwhelming majority of Americans a tax break is a 'lurch to the left.' It's certainly been moderate and centrist and focused on trying to make sure that this economy gets a jump start."
When asked by Schieffer if the Bush era tax cuts for the wealthiest 2 percent of Americans should be extended, he replied, "We should not have any tax increases. In an economy like this we don't need to be raising anybody's taxes."
Barbour said the issue for voters is "jobs, jobs, jobs, jobs,"
"If you look at the month before President Obama took office we were bleeding 750,000-plus jobs a month," Wasserman Schultz said. "Fast forward a year and a half later and we are adding about 100,000 a month in the private sector. We've made the auto industry profitable, We've turned things around."
She said voters in November will have a choice, they will choose to move forward and not "backslide toward the Bush era."