Both shifts, demographic and economic, must be addressed if Republicans are to find a way back to the majority. But the temptation for the party’s elites will be to fasten on the demographic explanation, because playing identity politics seems far less painful than overhauling the Republican economic message.

This explains why many high-profile Republicans responded to last Tuesday’s defeat by embracing some form of amnesty for illegal immigrants. Fox News’s Sean Hannity, a reliable weather vane, publicly converted to the cause of comprehensive immigration reform last week. The Washington Post’s Charles Krauthammer argued that if the Republican Party embraced amnesty and nominated Marco Rubio, it would win the Hispanic vote outright in 2016, solving its demographic problem in one swoop. Judging from the noises emanating from John Boehner and Eric Cantor, the party’s Congressional leadership agrees.

No doubt a more moderate tone on immigration would help Republicans. But the idea of amnesty as a Latino-winning electoral silver bullet is a fantasy.

First, Hispanics are not single-issue voters: they can be alienated by nativism, but they can’t just be won by the promise of green cards and open borders. (After Reagan signed an amnesty bill in 1986, the Republican share of the Hispanic vote fell in the next presidential election.) Latino voters are not, as conservative strategists often claim, “natural” Republican voters — notwithstanding their (moderate) social conservatism, they tend to lean leftward on economic issues, and to see government more as an ally than a foe. They can be wooed, gradually, if Republicans address their aspirations and anxieties, but they aren’t going to be claimed in one legislative pander.

At the same time, a Republican Party that moves too far leftward on immigration risks alienating its white working-class supporters, an easily disillusioned constituency whose support the party cannot take for granted. These voters already suspect that Republican elites don’t have their interests at heart: Mitt Romney lost last week because he underperformed among minority voters, but also because a large number of working-class whites apparently stayed home. If the party’s only post-2012 adjustment is to embrace amnesty, they aren’t likely to turn out in 2016 either.

What the party really needs, much more than a better identity-politics pitch, is an economic message that would appeal across demographic lines — reaching both downscale white voters turned off by Romney’s Bain Capital background and upwardly mobile Latino voters who don’t relate to the current G.O.P. fixation on upper-bracket tax cuts.

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The good news is that such an agenda already exists, at least in embryonic form. Thanks to four years of intellectual ferment, Republicans seeking policy renewal have a host of thinkers and ideas to draw from: Luigi Zingales and Jim Pethokoukis on crony capitalism, Ramesh Ponnuru and Robert Stein on tax policy, Frederick Hess on education reform, James Capretta on alternatives to Obamacare, and many more.

The bad news is that unlike a pander on immigration, a new economic agenda probably wouldn’t be favorably received by the party’s big donors, who tend to be quite happy with the Republican Party’s current positioning.

But after spending billions of those donors’ dollars with nothing to show for it, perhaps Republicans should seek a different path: one in which they raise a little less money but win a few more votes.