"Sen. Kerry has a long history of liberal positions that are not consistent with a majority of Texans," Cornyn said in a statement. The senator is up for re-election next year and could face a tea party challenge.
Kerry's smooth path to the nation's top diplomatic job stands in stark contrast to the harsher treatment for Obama's other national security nominees — Chuck Hagel to be defense secretary and John Brennan to be CIA director.
Hagel, the former two-term Republican senator from Nebraska, faces strong opposition from some of his onetime GOP colleagues who question his support for reductions in the nuclear arsenal and cuts in defense spending. Lawmakers also have questioned whether he is sufficiently supportive of Israel and strongly opposed to any outreach to Iran.
Democrats have rallied for Hagel, and he has the announced support of at least a dozen members in advance of his confirmation hearing on Thursday. Six Republicans have said they would vote against him, with some opposing Obama's choice even before the president's announcement.
Brennan faces questions from the GOP about White House leaks of classified information and from Democrats about the administration's use of drones.
Sen. Lindsey Graham, R-S.C., threatened to block the nomination of both men until he gets more answers from the Obama administration about the assault on the U.S. diplomatic mission in Libya that killed Ambassador Chris Stevens and three other Americans.
Graham, who earlier this month signaled he would delay Brennan's pick, said in an interview Monday night with Fox News' "On the Record" the he would "absolutely" block Hagel unless Defense Secretary Leon Panetta testifies about the attack in Benghazi, Libya.
Clinton testified for more than five hours last Wednesday before the House and Senate, but that wasn't sufficient for Graham.