He said the measure only passed because "the playing field favored the president. If nothing were done, it would have been a tax increase on every American."
When asked about Obama's recent suggestions that there won't be debate about raising the federal debt ceiling in the future, Cruz chuckled.
"The president would like to keep taxing and spending as if the laws of arithmetic do not apply," he said.
Cruz said of the Newtown shooting, "It breaks your heart, it shouldn't happen, it's unimaginable." But he also pledged to lead the fight against legislation proposing a national gun registry — alleging that such registries could be used as "a preface for confiscation" of firearms.
Cruz was selected to the Senate Judiciary Committee as well as the Armed Services, Aging, Commerce and Rules Committees.
A former Ivy League debating champion, Cruz could become a rising star among Capitol Hill conservatives following the recent exit of tea party leader U.S. Sen. Jim DeMint of South Carolina, who resigned to lead the Heritage Foundation.
"Jim DeMint's leaving the Senate will leave an enormous void," Cruz said. "In many ways the most significant legacy is a new generation of leaders who are committed to economic freedom."
Described as the first Texan in the Senate who speaks without a twang, Cruz insisted his accent actually comes and goes based on his audience.
"It depends on who I'm talking to," he said.