Ask people what Mitt Romney's worst moment was in the 2012 campaign, and most will tell you the "47 percent" video.

Fair enough. But for me, the lowest moment for Romney -- and one that signaled the broader problems facing the Republican party in that election and the one to come -- was his awkward and politically tone-deaf answer when asked during a Florida debate to explain his immigration position.

"The answer is self deportation, which is people decide they can do better by going home than they can do here," Romney said, a comment that -- even in the moment -- drew laughs from the crowd.  It was clear what Romney was up to: Afraid of being labeled a moderate on immigration (and other) issues, he adopted an entirely indefensible position that not only didn't help him in the primary but, without question, hurt him in the general election.

Now, one of the senior staffers on Romney's race, deputy campaign manager Katie Packer Gage, is telling Republicans that to repeat the mistakes of her candidate could have disastrous implications in the 2016 general election. Writing in Politico, Packer Gage argues:

Using harsh rhetoric that defines anything short of deportation as "amnesty" — without any plan for real immigration reform — may receive applause at a town hall meeting in Concord, New Hampshire, or a house party in Cedar Rapids, Iowa. And it may be popular with a small number of GOP primary voters and conservative talking heads, but it doesn’t win the hearts of the majority of primary voters and it alienates critical general election constituencies ...

... It is true that there is a group of strident, anti-immigrant voters in early GOP primary states, but this group is not nearly as large as portrayed. Just 17 percent of Republicans in Iowa, 18 percent in South Carolina and 20 percent in New Hampshire are hard-line voters who want mass deportations and consider anything less than that to be a deal-breaker.

Packer Gage is citing data derived from polling and focus groups her firm conducted recently in Iowa, New Hampshire and South Carolina as well as 10 other general election swing states. And, there's little available data that seems to run counter to what she's found. Of the first three states to vote in 2012 -- Iowa, New Hampshire and South Carolina -- only in South Carolina did "illegal immigration" break into the top four of voters' concerns. Even then, just 3  percent of primary voters said illegal immigration was the issue that mattered most to them.

What's harder to quantify is how much a candidate's position on immigration serves as a sort of litmus test for his or her conservative bona fides with voters. Anecdotally, there seems to be some evidence that it does.  Remember that a large part of John McCain's collapse in the summer of 2007 was tied to his vocal support for immigration reform. Ditto the precipitous drop in Marco Rubio's poll numbers in the wake of his involvement in the Senate-passed comprehensive immigration reform plan in 2013.  That both men subsequently distanced themselves from their past support for reform -- and watched as their poll numbers bounced back accordingly -- adds some weight to the argument that immigration matters in a Republican primary.

[Rating the 2016 candidates’ many contortions on immigration]

Just how much a candidate's position on immigration matters to Republican caucus and primary voters will be directly tested in the 2016 campaign by Jeb Bush, who has refused to back off his support for immigration reform -- although, notably, he barely mentioned the topic during his announcement speech Monday.

Assuming Bush stands firm on his immigration position, it will force voters in early states to decide whether his position disqualifies him to be the nominee. If Packer Gage's data is right, the "amnesty" crowd is vocal but a lot smaller than most people think. If she's wrong, then Jeb isn't going to be the nominee.

Less up in the air is Packer Gage's point about the dangers of Republicans being labeled anti-immigrant when it comes to winning the White House next November. She writes:

53 percent of general election voters from key swing states would be less likely to vote for a candidate they viewed as anti-immigration. That dwarfs the 29 percent of likely general election voters who would be more likely to vote for an anti-immigration candidate ...

... The numbers don’t lie. To grow our party — and win the White House in November 2016 and beyond — Republican candidates need to resist the temptation to characterize one another as soft on immigration.

She's right — no matter how unlikely it is that Republican candidates heed her advice over the next six months. If you need proof, check out this chart, which breaks down the 2012 election between white and non-white votes.

For all the attention that Romney's dismal 27 percent performance among Hispanic voters received after the election, to me the more amazing number is that only 11 percent of people who voted for Romney in 2012 weren't white. That's unsustainable given the demographic growth (and shrinkage) patterns happening in the country.

Simply finding a way to talk in more accepting terms about immigration and immigrants won't turn those numbers around overnight. But as Packer Gage rightly notes, continuing down the path of trying to prove who can be the most stridently opposed to comprehensive immigration reform could leave the eventual Republican nominee badly damaged -- and not just with Hispanic voters -- before the general election even begins.