The Indiana governor, who may himself seek the nomination, repeatedly referred to the Religious Freedom Restoration Act signed by then-President Bill Clinton over 20 years ago and similar legislation once supported by then-Illinois state legislator Barack Obama. But ABC host George Stephanopoulos noted that at the time Obama supported the law, Illinois had a provision barring discrimination based on sexual orientation, something Indiana lacks.
And White House press secretary Joshua Earnest blasted Pence on the same show, saying the governor was "in damage-control mode … and he's got damage to fix." Earnest added that "it should be easy for leaders in this country to stand up and say that it is wrong to discriminate against people just because of who they love."
Read More Religious Freedom Restoration Act: What You Need to Know
The problem for Pence and Republicans is that the general public has evolved rapidly on the issue of gay rights while the activist base of the GOP has not.
The party's 2016 GOP candidates may now need to back the law in the primary process so as not to anger the religious right, notably Iowa caucus kingmaker Bob Vander Plaats, who strongly supports the measure. But support for the law could come back to damage the eventual nominee in a general election in which swing voters could be easily moved by charges of discrimination against gays.
The American evolution on the issue of gay rights cannot be overstated. In 1996, just 27 percent of Americans favored allowing gays to marry. That number is now 54 percent and rising. In a March 2013 Washington Post/ABC News poll, 69 percent of respondents opposed businesses being allowed to refuse to serve gays and lesbians.
And support skews to the younger voters whom a successful general election candidate will need to bring to the polls in November of next year. Nearly 70 percent of millennials support same sex marriage.
Read More The Indiana law that 'fell off the stupid tree'
Indiana's new law—and Pence's defense of it—brought a massive reaction from corporate and pop culture figures.
The NCAA, which holds the Final Four in Indianapolis this weekend, said it would have to rethink future events in the state. Apple CEO Tim Cook, who recently came out as gay, blasted the decision in a Tweet: "Apple is open for everyone. We are deeply disappointed in Indiana's new law and calling on Arkansas Gov. to veto the similar #HB1228." Indianapolis' own mayor ripped the law.
Read MoreTim Cook: 'Religious freedom' law bad for business