Ted Cruz is involved in a controversy as to whether he ever supported anything resembling a "path to citizenship" for illegal aliens. The record shows pretty clearly he did. He insists he did not. William Saletan explains the whole thing by just saying Cruz is lying and he links to other sources that agree. Even some folks you'd think would be on Cruz's side aren't buying his spin.
I don't think it'll affect Cruz's performance in this election one bit. You have Trump out there saying he saw thousands of people in New Jersey cheering 9/11. You have Carson telling tales of his past that no one believes. You have Fiorina tripling-down on that Planned Parenthood video that no one else has seen and on Obama firing that general who actually resigned during the Bush administration. I can buy that Christie's statement about being buddy-buddy with King Hussein of Jordan (who died years ago) was a brainfart or a misspeak but he's said plenty of things that just plain aren't true. They all have.
The effect of all this fibbing is that lots of folks are accepting that politicians lie so you have to vote for liars. They may even rationalize it as something that good men and women must do in order to get elected. We forgive our choices a lot. We don't fault them much for selling their souls to special interests for the money it takes to win. We don't fault them for dodging questions, the answers to which might cost them the votes to win.
My guess is that Cruz won't lose supporters because his supporters want results — in his case, because they want someone who'll treat illegal aliens and maybe all wanna-be immigrants like rabid dogs you don't want in your neighborhood. To them, Cruz looks like the candidate most likely to do that in the future, regardless of what he may have done in the past. So what if he felt he had to lie about that to win? Better a liar who'll "secure our borders" (a term which is increasingly becoming a euphemism for racial and religious purity) than an honest person who'll do all those awful, Commie/Sharia things described on the plaque on the Statue of Liberty.
They'll not only continue to back Cruz but they'll attack Hillary for being a liar. Only your guy gets a pass on that.