The latest example played out Thursday on the Senate floor, where two Republican senators rebuked a third — tea party favorite Rand Paul of Kentucky — for his filibuster that challenged U.S. policies for using drones to kill suspected terrorists. Just a few days earlier, other high-profile Republicans had differed on immigration, and a House committee chairman renewed his call for spending cuts that would go much deeper than those now making headlines.
Every case featured past or possibly future presidential candidates. It was a fresh reminder that the party has no clear leader, and no clear road map, after Mitt Romney's November loss to Obama.
The quarrels also underscore the Republican establishment's uneasy relationship with the tea party. That grass-roots movement, born in 2009, pumped new passion into the GOP, but it also fueled unwise Senate nominations that saved several endangered Democrats.
Every party undergoes self-examination and blame-swapping after losing a presidential race. The Republicans' intramural disputes may eventually lead to greater solidarity and popularity.
Some party activists, however, are warily watching Obama launch a new outreach to rank-and-file Republicans, including his Wednesday night dinner with a dozen GOP senators at a posh Washington restaurant.
"The president recognizes the fractures within the Republican Party and is moving to try to take advantage of them with a charm offensive," said GOP pollster Steve Lombardo. Republicans should react carefully, he said, because voters "want to see each side extend an olive branch and work together."
First, however, top Republicans must resolve some of their own differences. And either by choice or trial-and-error, the GOP must decide how closely to align its identity with the tea party movement, whose fiercely small-government philosophy draws relatively low approval ratings in national polls.
Paul, the son of libertarian hero and three-time presidential contender Ron Paul, drew widespread attention this week with a nearly 13-hour Senate filibuster. He demanded assurances from the Obama administration that unmanned aircraft would not be used in the United States to kill terrorism suspects who are U.S. citizens.
Many Republicans say Paul and his father are so libertarian in their outlook that they operate outside the party mainstream. But Paul's filibuster drew active support from several tea party-leaning senators, including Marco Rubio of Florida, who possibly could vie with Paul and others for the 2016 presidential nomination. Also helping with the filibuster were more traditional Republican senators such as John Cornyn of Texas and John Thune of South Dakota.
That sharpened the drama Thursday, when Republican Sens. John McCain of Arizona and Lindsey Graham of South Carolina claimed the Senate floor to chide Paul and to defend the administration's drone policies.
McCain, the party's 2008 presidential nominee, and Graham are frequent guests on national talk shows. They rank among the party's best-known members, and they attended Obama's dinner Wednesday.
Their critiques of Paul's actions were acidic at times. McCain read approvingly from a Wall Street Journal editorial titled "Rand Paul's Drone Rant." McCain said Paul's reasoning did not match his "showmanship."
McCain and Graham are among pro-military Republicans unhappy with a tea-party-backed push to cut spending across the board, including in the Pentagon. The recently enacted "sequester" cuts were seen as a triumph for conservatives, especially in the House, who place their highest priority on refusing to raise income taxes on anyone, even if it means reducing military spending.
These House Republicans, led by 2012 vice presidential nominee Paul Ryan of Wisconsin, now promise to pass a 10-year budget plan that will call for much deeper spending cuts, including significant changes to Medicare.
The move carries risks, say moderate Republicans. They cite polls showing substantial public support for a balance of tax increases and spending cuts to tame the deficit.
A survey by the centrist Republican Main Street group found that most Americans feel the Republican Party chiefly "looks out for rich guys," said the organization's president, Steve LaTourette. The former Ohio congressman said the party's self-examination, on balance, is healthy and essential, and he thinks Republicans outflanked Democrats in the sequester showdown.
Virginia-based Republican consultant Chris LaCivita said the intraparty debate is healthy and should reassure voters the GOP is vigorous and transparent.
Obama is appealing to Graham and other Republicans who say new taxes on the rich might be possible if Democrats agree to tackle the long-term funding problems of Medicare and Social Security. Most Republican leaders adamantly oppose any increases in income taxes.
Other internal debates that Republicans must resolve include gun control and immigration. Sen. Charles Grassley of Iowa was the only Republican on the Judiciary Committee this week to vote with Democrats to make it a felony to buy a gun for someone who could not pass a background check.
Regarding immigration, Romney and other GOP candidates did poorly among Hispanic voters, many of whom see the party's immigration policies as a slap at all Latinos.
Rubio, the son of Cuban immigrants, is heading a Republican effort to craft immigration legislation to counter Obama's proposals.
Another prominent Republican, former Florida Gov. Jeb Bush, created a stir this week by saying he did not support a pathway to citizenship for illegal immigrants, even if they have lived peacefully for years in the United States. Bush, whose father and brother were presidents, tried to soften the comments later, but they served to remind everyone that Republicans face difficult debates over immigration.
The 2016 presidential race could possibly attract Bush, Rubio, Ryan, Paul, Thune and numerous other Republicans, including Govs. Chris Christie of New Jersey and Bobby Jindal of Louisiana.
The 2012 Republican primary featured exhaustive and often unwieldy debates. Catering to hard-core conservatives who dominate primaries, Romney and his rivals veered to the right on many issues, a process that many feel hurt Romney among centrist voters in the general election against Obama.
With tea party-backed House Republicans thus far dominating the tax-and-spending debate, it's unclear whether the GOP can avoid similar clashes in 2016. Before it confronts that question, however, the party must move closer to consensus and intraparty peace over immigration, anti-terrorism and other matters.
This week's back and forth in the Senate indicates the soul-searching will go on a while longer.