Texas Sen. John CornynJohn CornynSenators who have felt McCain's wrath talk of their respect for him Senate heads to new healthcare vote with no clear plan McCain absence adds to GOP agenda’s uncertainty 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 PaulRand PaulThe Hill's 12:30 Report Senate heads to new healthcare vote with no clear plan Overnight Healthcare: CBO predicts 22M would lose coverage under Senate ObamaCare replacement 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.