Texas Sen. John CornynJohn CornynMcCarthy: ‘No deadline on DACA’ NSA spying program overcomes key Senate hurdle Hoyer suggests Dems won't support spending bill without DACA fix MORE promised to work for a GOP Senate majority in 2012 after he was unanimously reelected Tuesday as chairman of the National Republican Senatorial Committee.

Singling out the support of the "13 new Republican senators" he helped elect, Cornyn promised "continuity."

"Continuity at the NRSC is something we haven't had in a while, and which we need to build on our victories in 2010," he said in a statement.

Observers have speculated the rise in prominence of Sen. Jim DeMint (R-S.C.) and the election of Tea Party-backed senators such as Rand PaulRandal (Rand) Howard PaulNSA spying program overcomes key Senate hurdle Fix what we’ve got and make Medicare right this year Despite amnesty, DACA bill favors American wage-earners MORE of Kentucky could cause tension in the caucus.

Cornyn urged his colleagues to collaborate.

"I believe Republicans are strongest when we stick together, and I continue to adhere to the words of William F. Buckley, who famously said: 'I am for the most conservative candidate that can get elected,'" he said. "But I recognize that Republican primary voters choose our nominees, and I am committed to listening to the message voters sent this past year."

Cornyn had no competition for a second term.