One of the first people to congratulate former solicitor general Ted Cruz on his victory in the Texas Republican Senate runoff on Tuesday was fellow Texan (and Republican Senator) John Cornyn.

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Cornyn said he “could not be more pleased with the nomination” of Cruz. Cornyn, who also happens to be the chairman of the National Republican Senatorial Committee, remained neutral throughout the primary and won’t need to worry about Cruz holding the GOP seat in November.

That said, Cruz’s victory will almost certainly make Cornyn’s life — and the lives of the other members of the Senate Republican leadership more difficult.

Here’s why.

As chairman of the NRSC, Cornyn belongs to one power center in the chamber — one primarily concerned with majority making . Conservative Sen. Jim DeMint (R-S.C.) belongs to an alternative one, which is concerned with building a coalition of conservative senators.

And that reality means DeMint has even more reasons than Cornyn to celebrate Cruz’s win.

DeMint, a conservative icon who proved to be quite the thorn in Cornyn’s side last cycle, backed Cruz in the primary. DeMint’s Senate Conservatives Fund and its super PAC spent $2 million to help Cruz take down Lieutenant Governor David Dewhurst, a onetime overwhelming favorite and the candidate preferred by the state’s GOP establishment including Gov. Rick Perry .

Cruz’s primary win virtually ensures that DeMint will have another constitutional conservative ally in the upper chamber during the next Congress. And if Republican nominee Richard Mourdock wins in Indiana, that’s at least two conservatives who have shown a willingness to buck the establishment from the right who are coming to the Senate next January. (It is worth noting that DeMint did not endorse Mourdock’s primary challenge against Sen. Richard Lugar.)

They will join Sens. Mike Lee (Utah) and Rand Paul (Ky.) in DeMint’s rump caucus within the Republican Senate conference.

To be clear, Cruz’s win doesn’t change the fact that Republicans are overwhelmingly favored to hold the seat being vacated by retiring Republican Sen. Kay Bailey Hutchison (R). But past posturing by Cruz suggests that Cornyn’s relationship with him may not be identical to the one that Dewhurst would have shared with the NRSC chairman.

Earlier this year, even as all of the other major candidates in the Texas Republican field pledged to support Cornyn for the number two post in the Senate GOP hierarchy next year, Cruz told a radio station it would be “presumptuous” for him to endorse before being elected.

National Democrats, meanwhile, used Cruz’s win to fan the flames among Republicans, arguing that former state solicitor general’s win will make for an (even) more unpredictable GOP conference.

“Mitch McConnell is now going to have a potentially much more tea party- oriented caucus,” Democratic Senatorial Campaign Committee Chair Patty Murray (Wash.) told reporters on Wednesday morning in the aftermath of the Cruz win.

Still, there is reason to believe that Cruz, a likely rising national star, might want to cast wide net of alliances in the Senate, including a warm relationship with Cornyn. He may very well chart a path resembling the one Sen. Marco Rubio (R-Fla.) — to whom Cruz is often compared — has opted to take. Unlike DeMint, Rubio hasn’t been a partisan bomb-thrower and does not appear to want to be classified as being purely a conservative ideologue. Cruz is still young and may want to craft a profile that extends beyond pure partisanship.