WASHINGTON » For the past two years, Republican senators facing re-election have very deliberately spent millions of dollars, hired multiple consultants and cast scores of conservative votes with one goal in mind: avoiding the embarrassing primary conflagrations that befell their party in 2010 and 2012 and cost Republicans a chance at taking back the Senate.

It has not worked. Despite their concerted and careful efforts, some of the best-known and most influential Republicans in the Senate have been unable to shake threats from the right and have attracted rivals who portray these lawmakers as a central part of the problem in Washington.

In Kentucky, Mitch McConnell, the party’s Senate leader, is fending off a charismatic and wealthy conservative challenger. In South Carolina, Lindsey Graham, one of the Senate’s most reliably conservative voices on foreign policy, is being painted by primary opponents as a veritable clone of President Barack Obama.

In Tennessee, Tea Party activists have vowed to take out Lamar Alexander, the veteran senator, former Cabinet officer and two-time presidential candidate.

"Sen. Alexander has never been a true conservative," said Ben Cunningham, president of the Nashville Tea Party. "His support for the amnesty bill has caused great problems for us," he said, referring to the Senate immigration bill. "He is at best a moderate."

Tea Party candidates have also emerged in races against Democratic incumbents in Alaska — Joe Miller, who beat Sen. Lisa Murkowski in her previous primary, has resurfaced — Colorado, Louisiana and North Dakota, and for open seats in Georgia, Iowa and South Dakota. Democrats hope they can benefit from a divided Republican electorate.

The Republican incumbents and party officials say they have learned from the hard lessons of the past when Tea Party candidates from the right were ignored or dismissed, only to prevail in primaries and lose in general elections. They have plans to avoid becoming the next Dick Lugar or Robert Bennett, two senior senators who were stunned by losses before the general election.

As such, the races are emerging as the real test of the latest Republican strategy to deal with insurgent candidates and of the power of the Tea Party in 2014. The result could dictate not only the future influence of the Tea Party in Congress, but also the ability of Republicans to hold on to or gain seats.

"People talk about how unorganized the Tea Party is," said Al Cross, director of the Institute for Rural Journalism and Community Issues at the University of Kentucky. "Well, it’s organized enough to pull people together."

These challenges are not without costs. Republican incumbents often move to the right to fend off a primary fight from that wing, which only emphasizes party infighting over core issues like immigration and how best to tackle fiscal fights on Capitol Hill, often damaging them in a general election.

The costs are monetary as well as political. McConnell is now forced to fight on two fronts simultaneously and early against Matt Bevin, his Republican challenger, and Alison Lundergan Grimes, a Democrat, and has already spent $700,000 on advertising.

Republicans say candidates have left nothing to chance. They have spent time courting conservative groups, hired consultants who helped Tea Party-influenced senators win in the last cycle and, at least in McConnell’s case, worked hard to define challengers early, rather than ignoring them and praying for an industrial accident.

What is more, Republican officials note that many Tea Party groups have tried to field contenders in South Dakota and West Virginia, and come up short. In Arkansas, a big pickup opportunity for Republicans, the party has united behind Rep. Tom Cotton, a Harvard-educated combat veteran who is planning to try to unseat the incumbent Sen. Mark Pryor, a Democrat.

So far, Sen. John Cornyn of Texas has escaped any challengers in spite of Sen. Ted Cruz’s victory there over an establishment Republican in 2012. That has not kept Cornyn from attending numerous Republican county dinners this summer and meeting with grass-roots activists.

This time challengers have far higher to climb.

"Part of the reason incumbents are in very good shape in their states is because they have governed conservatively," said Brad Dayspring, the spokesman for the National Republican Senatorial Committee.

Incumbents say that the conservative purity craved by Tea Party groups is not attainable and that their records are more than appealing to Republican voters.

"I expected to be challenged," Graham said. "I think I have a good story to tell about my record as senator. I’m proud of the fact that I try to solve problems. Like Ronald Reagan, if I get 80 percent of what I want, I call it a good day."

These Republicans, determined to not scotch yet another opportunity to retake the Senate, have taken steps to avoid being picked off by a challenger from the right.

After supporting Sen. Rand Paul’s opponent in 2010, McConnell has done a complete about-face, voting for Paul’s austere budget measure and working with him to legalize domestic hemp production. His campaign manager ran Paul’s 2010 campaign and was a top aide on Ron Paul’s presidential campaigns.

In Tennessee, Alexander lined up endorsements from conservative groups and wrapped up the support of Gov. Bill Haslam and the conservative House members Marsha Blackburn, Diane Black and Phil Roe, among others, and has raised $3 million already.

Alexander and his supporters have been playing up his record as governor, when he paid cash for road construction to prevent the state from going into debt. He has also written an open letter to voters laying out his conservative record, facing Tea Party criticism head on.

"I think Lamar’s going to be fine," said Sen. Bob Corker, the junior senator from Tennessee.

Senators have also moved to the right on the Senate floor. McConnell voted with conservatives against the Violence Against Women Act and was among a mere 13 senators to vote for a measure by Paul to cut off aid to Egypt. Cornyn opposed the confirmation of his former Senate colleague John Kerry, one of a mere three senators to cast a "no" vote for the secretary of state.

In a meeting with libertarians the other day in Mount Pleasant, S.C., Lee Bright, a state senator challenging Graham, made the case that Graham was overly concerned with international affairs and too soft on gun rights, personal liberties and immigration to remain in office.

"He said he doesn’t care if the NSA has his phone number," Bright said, referring to the National Security Agency. (Bright has sponsored legislation to give South Carolina its own currency and opposing Sharia.)

Bright and others could give Graham trouble if they force him into a runoff, Republican political experts said. But in the end, they imagine incumbency plus running to the right will pay dividends.

"In 2006, Lindsey Graham got booed at a Silver Elephant dinner," said J. Hogan Gidley, the former executive director of South Carolina Republican Party, referring to an activist conservative group. "Fast forward to 2013 and the entire room gave him a standing ovation at same dinner. If you come back and you’re cheered, you’ve done something right."