Cruz acknowledged that change wasn't likely to happen, because it lacks the support of Senate Majority Leader Mitch McConnell, R-Ky., who he has quarreled often with in the past.
"We don't have the votes in the Republican conference," said Cruz. "I don't know if we even have half of Republicans who would support changing the filibuster."
That hasn't stopped Cruz from pushing other ideas unpopular with his party, and he points to some success.
During tax negotiations last October, Cruz said he personally pitched the idea of stripping Obamacare's individual mandate through the tax bill. Fresh off a string of embarrassing failures in their attempts to repeal the law, Cruz said party leaders didn't want to "muck up tax reform by getting back into" health care.
"Last October I began pitching (it). ... It was me and a half-dozen conservatives," said Cruz. "Most of the conference was skeptical ... We began making the case both privately within the conference and publicly to the American people."
All Republican senators later voted to include the measure, which Cruz called "one of the major victories in tax reform."
Cruz is one of just two Senate Republicans facing a serious challenge from a Democrat in 2018, along with Sen. Dean Heller, R-Nev. Republicans are defending just eight of the Senate seats up for re-election. Democrats are defending 24 seats, as well as two independents who caucus with them.
Cruz was elected to the Senate in an upset primary victory in 2012, then went on to finished second in the GOP presidential primary four years later. He avoided a major challenge from his own party in his first re-election race to the Senate. Texas's primary will be held March 6.
(c)2018 McClatchy Washington Bureau
Visit the McClatchy Washington Bureau at www.mcclatchydc.com
Distributed by Tribune Content Agency, LLC.