Republicans have been talking about reforming their party since President Obama's re-election in 2012. The recent Supreme Court rulings on same-sex marriage and Obamacare and the reversal of several Southern Republican governors on the Confederate battle flag gave the GOP a new chance. But change can be hard.

In presidential years, the party has a math problem, according to GOP strategist Steve Schmidt. He points out that while Democrats are attracting growing segments of the population, like Latinos and Asians, Republicans are relying on their traditional base of white voters.

"Every single demographic group in the country that is growing, Democrats are growing their market share," said Schmidt, who ran John McCain's ill-fated 2008 presidential campaign. "Every single demographic group that is shrinking, Republicans are growing their market share. That's a fundamental marketing problem."

And that's partly why the GOP has lost the popular vote in the last five of six presidential elections. But it's hard for Republicans to broaden their appeal to young people or Hispanics, for instance, when there's a big split inside the party on issues like same-sex marriage or immigration. And Republicans haven't even decided exactly how they need to change.

'There's An Old Saying About Wrestling A Pig'

The party's task of improving its image with Hispanic voters was made more difficult recently by the candidate who has been polling near the top of the field in Iowa, New Hampshire and national polls: Donald Trump.

"When Mexico sends its people, they're not sending their best," Trump said last month, announcing his presidential candidacy. He added, "They're bringing drugs; they're bringing crime, [bringing] their rapists. And some, I assume, are good people."

Trump, whose political persona is built around being outrageous, ended up reinforcing the most negative perceptions of Republicans. There was a huge backlash as companies like NASCAR, Univision, NBC and Macy's rushed to cut ties with him.

Over the weekend, Trump acknowledged his run may be turning out to be bad for business.

"I think it's bad for my brand," Trump said, adding, "I lose customers; I lose people."

And then there was this: Trump reportedly retweeted (then deleted) this: "#JebBush has to like the Mexican Illegals because of his wife."

But reaction from the Republican presidential candidates took weeks, and when it came did come, it was mixed — or late.

"There's an old saying about wrestling a pig — both of you get dirty, and the pig likes it," Schmidt said. "And there's something of that going on."

Schmidt weighed in last week when only Jeb Bush had weighed in, before other candidates came out late last week or over the weekend with their denouncements, or in one candidate's case, praise.

Bush answered a question, asked and answered in Spanish, about Trump's remarks after a town hall meeting last week in Nevada.

"I disagree with his remarks," Bush said in Spanish. "They do not represent the values of the Republican Party, and they do not represent my values."

At an event in New Hampshire over the holiday weekend, Bush was more forceful, calling the comments "ugly" and saying he "absolutely" took personal offense.

"He's doing this — he's not a stupid guy," Bush said, "so I don't assume he thinks that every Mexican crossing the border is a rapist. He's doing this to inflame and incite and to draw attention, which seems to be the organizing principle of his campaign." He added, "[P]olitically, we're going to win when we're hopeful and optimistic and big and broad rather than errrrr, grrrr, just angry all the time. This is an exaggerated form of that, and there is no tolerance for it."

Former Texas Gov. Rick Perry said Thursday on ABC that he was "offended" by Trump's remarks.

"I've said very clearly that Donald Trump does not represent the Republican Party," said Perry, who landed in controversy over immigration in 2012 because Texas allows in-state tuition for immigrants in the U.S. illegally.

Florida Sen. Marco Rubio also called the comments "offensive," "inaccurate" and "divisive." New Jersey Gov. Chris Christie called them "inappropriate."

Texas Sen. Ted Cruz, a candidate who argues that the party needs to return to its consistently conservative roots, defended Trump's comments, in a way.

"I salute Donald Trump for focusing on the need to address illegal immigration. The Washington cartel doesn't want to address that," he said on NBC's Meet the Press. "He has a colorful way of speaking. It's not the way I speak. But I'm not going to engage in the media's game of throwing rocks and attacking other Republicans."

In waiting so long to respond, though, the damage may have been done, former RNC Chairman Michael Steele argued.

"You're not coming out on something that everyone in the country reacted to this, and you didn't, the party didn't, and those who want to be president didn't until, what, this week?" he said on Meet the Press.

Change The Pizza, Not The Box

There has been a continual argument in the party about tone versus substance, strategists say. Some in the party, like Cruz, argue that the GOP is too moderate, that it took its chance on the "moderate" candidates in 2008 and 2012 in McCain and Mitt Romney — and they lost.

But these reform-minded strategists think that argument is off base.

"Republicans have been arguing since 2012 about — do we need to change the pizza or do we need to change the pizza box?" said David Frum, a former speechwriter for George W. Bush. "And I think the correct answer is we need to change the pizza."

He added that it's not enough to change the tone with friendlier, less divisive rhetoric. Frum thinks Republican policies need to change, too. And that, he said, means accepting that Obamacare is not going away, same-sex marriage is now the law of the land, and that 11 million immigrants who are here illegally are here to stay.

Frum said the party has made some progress, on "one cultural issue" but has been slower on another.

"The Confederate flag — we have seen emphatic and decisive change," Frum said. "On another cultural issue — same-sex marriage — we have seen slow evolution that has touched much of the party but isn't yet articulated by the leading presidential candidates."

It's hard, though, to get the Republican Party in sync with the majority of voters on immigration reform, same-sex marriage or climate change when the Republican primary electorate is heading in the opposite direction, the strategists note.

Democrats, watching from the wings, are barely able to contain their glee.

"A lot of Republicans may talk about having new ideas and fresh faces, but across the board, they are the party of the past, not the future," Hillary Clinton said at a rally in Virginia last week to applause.

It's still early. Republicans have time to show voters they are a modern, future-oriented party. But if the image of Republicans as anti-immigrant, anti-gay and anti-science sticks, it will be a problem for the GOP next year.

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