Washington (CNN) - Most Republicans agree: Major changes are needed if the party wants to be competitive in future presidential elections.
But a new poll of Republicans nationwide also indicates that there's little agreement on the direction the GOP should take.
The Wednesday release of the Pew Research Center survey comes amid a very public squabble between possible 2016 presidential contenders Sen. Rand Paul of Kentucky and New Jersey Gov. Chris Christie that illustrates the difference among Republicans between sticking to conservative principles or trying reach out to the growing segment of minority and younger voters.
With losses from the last two presidential elections still stinging, two-thirds of Republicans questioned in the poll say that to do better in future presidential contests, the GOP needs to address major problems. Three in 10 disagree, saying the party just needs to address minor problems. Along those lines, nearly six in 10 say the party needs to reconsider some positions, with 36% saying the GOP needs to make a stronger case for its current policies.
But there's less agreement on what the party needs to do.
By 54%-40% margin, Republican and Republican-leaning voters say party's leaders should move in a more conservative direction, with four in 10 urging a more moderate direction.
"Not surprisingly, conservatives and those who agree with the Tea Party overwhelmingly favor moving in a more conservative direction, while moderates and liberals would like to see the party take more centrist positions. Yet the more moderate wing of the party is a minority generally, and makes up an even smaller share of the likely primary electorate," says a release from the Pew Research Center.
Has the GOP compromised too much or too little?
The poll indicates Republican voters are divided, with 35% saying the party has compromised too much with Democrats, 27% saying not enough, with 32% saying party leaders have handled this about right. More than half of tea party Republicans questioned say there's been too much compromise, with that number falling to just 22% among non-tea party Republicans.
The new numbers come as Paul and Christie have fired away at each other in a war of words that began last week when Christie, at a forum with other GOP governors, slammed Paul for his criticism of government surveillance to battle terrorists.
"This strain of libertarianism that's going through parties right now and making big headlines I think is a very dangerous thought," Christie said.
Asked if Paul was one of the people he was pointing towards, Christie added that "You can name any number of people and he's one of them."
Paul pushed back, and the fight continued Tuesday.
"I'm the one trying to grow the party by talking about libertarian ideas of privacy and the Internet and attacking me isn't helping the party. He's hurting the party," Paul said in an interview with CNN's Wolf Blitzer on "The Situation Room."
Paul has accused Christie of harming national security by hoarding federal relief money for Hurricane Sandy victims.
Christie has called on Paul to cut federal pork barrel spending in Kentucky.
"But I doubt he would because most Washington politicians only care about bringing home the bacon so that they can get re-elected," Christie charged Tuesday morning.
"This is the king of bacon talking about bacon," Paul responded later in the day on "The Situation Room."
Could this be a coming attraction of future intra-party fights?
"The Republicans are going to have a very spirited debate," says CNN Chief National Correspondent John King. "They have to deal with the immigration issue again. They have that ditch with Latino voters. Taxes and spending."
King says Christie and Paul are leading the fight right now, but that, "This is just the beginning. This is not going to stop."
"I think we are going to end up with a Republican primary that looks a lot like a cage match," says GOP strategist and CNN contributor Ana Navarro.
Another reason for the squabble: There's no one person leading the party right now. When asked in the poll who is leading the GOP, 56% of Republicans said that either nobody was or that they didn't know. One in 10 named House Speaker John Boehner as the leader, with other names offered all scoring in single digits.
The poll indicated that among seven leading Republican politicians questioned, Rep. Paul Ryan of Wisconsin had the highest favorable rating. Nearly two-thirds said they see the 2012 GOP vice presidential nominee and House Budget chairman in a favorable light. Paul was second, at 55%, with Sen. Marco Rubio of Florida, another possible White House contender, at 50% and Christie at 47%.
"If I was asked who the leader of the Republican party is right now I couldn't give you the name of that person," adds Navarro.
In an effort to rebuild their brand, the Republican National Committee last week announced a"50 state strategy" to deploy paid field staffers in every state to reconnect with voters.
"Republicans are united in helping the middle class, rebuilding the economy and tackling Obama's debt. We are busy establishing a permanent campaign to connect with voters in communities across all 50 states so candidates up and down the ticket will reap the benefits," RNC Press Secretary Kirsten Kukowski tells CNN.
The Pew Research Center poll was conducted July 17-21, with 497 Republicans and independents who lean towards the GOP questioned by telephone. The survey's sampling error is plus or minus 5.1 percentage points.