Roaming the stage in the cavernous basketball arena, Cruz said the health care law is exhibit A of secularism that poses a threat.
"Religious liberty has never been more under attack," Cruz said.
Cruz, who last year led a partial government shutdown over the national health care law, took aim over legal action by the Obama administration against nuns who oppose covering birth control for employees.
He also said business owners of faith are also being forced to provide health coverage that runs counter to their beliefs.
"So am I compelled to carry the gospel of freedom beyond my hometown," Cruz said, quoting civil rights leader Martin Luther King to the gathering of students and faculty in the campus arena.
Should he run, Cruz's faith-centered message could help win him support from a key group.
"He'd get a very strong following almost immediately," said Micah Nihart, a Liberty junior.
Cruz, a first-term senator, has been open about his Christian faith but has tended to focus publicly on constitutional and fiscal issues more than social ones. In recent weeks, he has not shied from social policy.
Last month, Cruz told an influential group of home-school advocates in Iowa that the United States was founded on Christian values. He also told a separate group of anti-abortion rights activists in Washington that they should not compromise on their beliefs.
In coming weeks, Cruz plans to speak to a "Freedom Summit" in New Hampshire, the early voting state, along with potential rivals Sen. Rand Paul of Kentucky and former Arkansas Gov. Mike Huckabee.
Cruz also plans to attend a Free Enterprise Foundation dinner a few days later at The Citadel in yet another early voting state, South Carolina.
The targeted outreach to different segments of the Republican Party is necessary if Cruz is going to expand his appeal beyond the tea party-aligned wings of the GOP that consider him among the favorites at this early stage of the 2016 contest.
Elliott reported from Washington.