Will challenges from right hurt GOP chances to retake Senate? Sen. John Cornyn, R-Texas, faces a primary challenge from conservative firebran Rep. Steve Stockman. Cornyn is the seventh Republican Senator facing a primary challenge from the right Democrats must defend 21 of the 35 Senate seats up for re-election in 2014 Strategists say earlier tea party backed challengers have hurt GOP Washington (CNN) -- Sen. John Cornyn, welcome to the club. The two-term Texas lawmaker is now the seventh Republican Senator up for re-election next year to face a primary challenge from his right. That club also includes the top Republican in the chamber, Minority Leader Mitch McConnell of Kentucky, Lamar Alexander of Tennessee, Thad Cochran of Mississippi, Mike Enzi of Wyoming, Lindsey Graham of South Carolina, and Pat Roberts of Kansas. If this seems like deja vu all over again, it is. Since the birth of the tea party movement in 2009, primary challenges from the right have made major headlines, and have hurt the GOP's efforts in the last two elections in their attempts win back control of the Senate from the Democrats. "Republicans effectively gave away five Senate seats the last two cycles because of candidates who weren't capable of winning in November," said Brian Walsh, who served as communications director for the National Republican Senatorial Committee, which provides support, advice and funding to Republican candidates, during the 2010 and 2012 cycles. Dems defending 21 seats With Democrats holding a 55-45 majority in the Senate but defending 21 of the 35 Senate seats up for grabs in the 2014 midterms, the GOP has another opportunity to try and retake the chamber. But Walsh said that he doesn't see a repeat of what occurred in recent years even though a majority of Republican Senators running for re-election are facing primary challenges. With the exception of perhaps Georgia, it's difficult to see that repeat itself even with the large number of primaries because many are not serious at this point. But Republicans have a tremendous opportunity to win back control of the Senate next year and it's a critical reminder to Republican primary voters that candidate quality matters," he told CNN. A top Senate Democratic official disagrees. Republicans said they needed to rebrand and start reaching out to voters in the middle in order to win. They were right, but the primaries have prevented them from doing that. Instead, primaries are forcing all Republican candidates to embrace the tea party and a slate of policy positions that will hurt them in a general election," said Matt Canter, deputy executive director of the rival Democratic Senatorial Campaign Committee. Six-term Sen. Cochran will run again in 2014 While the jury's out on what will happen next November, the new round of primary challenges from candidates enjoying support from tea party activists appears to be proof that the movement continues to strongly influence the Republican Party, even after some political pundits prematurely wrote the tea party's obituary after 2012. Major player in primaries Just as tea party backed lawmakers helped drive the unsuccessful push to defund the federal health care law, which helped to ignite the government shutdown in October, the group appears to once again be a major player when it comes to next year's primaries. The tea party gave voice to millions of Americans who understandably viewed Washington as an insular town determined to serve its own. As that old model breaks down, conservative influence in Washington will continue to grow," said Dan Holler, communications director for Heritage Action for America, which supports conservative causes and legislation but does not back individual candidates in primary challenges. Cornyn faces challenge he tried hard to avoid He becomes first GOP Senator to be challenged in a primary by a sitting member of Congress. In this case, it's Rep. Steve Stockman, a conservative firebrand who served one term in the 1990s before winning a ticket back to the House in last year's election. Since returning to Capitol Hill, Stockman's grabbed headlines for his calls to impeach President Barack Obama. Tea Party activists have been angry with Cornyn since earlier this fall, when he didn't support fellow Texas Sen. Ted Cruz when he led the push to defund Obamacare with a marathon filibuster on the Senate floor. Cornyn told reporters on Tuesday that he's not surprised about the challenge, but that Stockman "wasn't on my radar screen." Kentucky governor: McConnell's Obamacare criticism will hurt him While Stockman could find support among the ever increasingly conservative GOP electorate in Texas with its March primary just a few months off, he faces long odds against Cornyn, who has some $7 million cash on hand, compared to just $32,000 in the bank for Stockman. Large incumbent war chests Cornyn, like McConnell, has built large war chests in order to beat back primary challenges. And both men have hired veterans of the tea party movement to run their re-election campaigns. If you look at the two Republican incumbents who lost the last two cycles, arguably they didn't take their primaries seriously enough and weren't prepared. That's not the case this cycle where no one is taking anything for granted," Walsh added. Last year, Cruz upset Texas Lt. Gov. David Dewhurst, who had establishment backing, to capture the GOP Senate nomination, before going on to win the Senate seat in the general election. Cornyn says he's learned some lessons from that and other recent contests. I think Senator Cruz was unique in many ways because of his talents and the quality of the race he ran and the timing. So, I think one race does not a trend set but obviously there are lessons to be learned from that and believe me I've learned them," Cornyn said. CNN Congressional Producer Ted Barrett contributed to this report