The problem goes like this. The Democrats have the support of ethnic minorities and those who feel dependent on the state. Given the continuing mass immigration into America, and the growth of welfare dependency, this provides a growing electoral base for the left-liberal party.
The Republicans have to rely on a white/employed/married base. You might think, therefore, that the Republicans would not want to undermine this base through large-scale immigration. But right-liberals generally have an ideological commitment to immigration. They tend to see it favourably in terms of the workings of the market and as an aspect of "freedom" (of the actions of self-made individuals).
This right-liberal approval of large-scale immigration is apparent in the farewell address of Ronald Reagan:
...I've spoken of the shining city all my political life, but I don't know if I ever quite communicated what I saw when I said it. But in my mind it was a tall proud city built on rocks stronger than oceans, wind-swept, God-blessed, and teeming with people of all kinds living in harmony and peace, a city with free ports that hummed with commerce and creativity, and if there had to be city walls, the walls had doors and the doors were open to anyone with the will and the heart to get here. That's how I saw it and see it still...
Everybody getting their chance in the market to become 'self-made' is the aim. (What makes Reagan sound patriotic here is that he puts the vision in positive terms, whereas someone on the left might talk about guilt and oppression.)
But this idea of America being "open to anyone" makes the task of winning elections for the right-liberal party more difficult with each passing year. For a time the right-liberals can mobilise the white/married/employed/conservative voting base, but eventually that base will shrink as a proportion of voters and prove inadequate. The Reagan vision of a shining city is not viable in the long-term for a right-liberal party.
Those on the left are aware of the shifting ground. For instance, back in May an article published by the Brookings Institute declared confidently that minorities would decide the 2012 election:
Obama and the Democrats believe demography is on their side. Census 2010 made abundantly clear that racial and ethnic minorities, especially Hispanics, are dominating national growth and will for decades to come. The Democratic agenda— favoring broader federal support for medical care, housing, and education seems designed to curry the favor of these groups, which played a huge role in tipping the balance in his favor in several key swing states.