Syrian refugees are near, the Cuban boatlift is far.
Construal level theory tells us that the further something is from us in time and space, the less likely we are to spot deformities, details, and defects. But with distance we are better able to identify patterns, shapes, and trends. My excellent friend Robin Hanson summarizes here, but also has a great deal more to say on the subject.
The 20th century (am I the only person who struggles mightily to resist capitalizing that?) is dismally full of refugee crises. A lot of them were African: Congo, Angola, Eritrea, Somalia, Liberia, Rwanda/Burundi, Sudan & al. These were tragic, but largely invisible to typical Americans, except perhaps as passing human interest stories, quickly forgotten in the noise of the celebrity scandal du jour. Some of them directly involved US concerns, as a great deal of displaced people ended up in the Land of the Free. Remember the Salvadoran Civil War spanning the Carter administration? Something like half a million Salvadorans ended up settling here. And that's just little itty-bitty El Salvador. The Mariel boatlift totaled over 100k Cubans over the course of 1980. Vietnamese refugees and their descendants following the end of the war account for roughly a million and a half of today's Americans. Khmer Rouge survivors stateside number roughly 300,000.
Are these regrettable? I was alive (though admittedly quite young, so my memory may be fuzzy) for several of these episodes, so I recall some of the contrary sentiment. In near mode, a refugee crisis sparks panic in recipient countries. How shall we feed them? Where shall we put them? What about medical care? Educating their kids? If anything, the opening act of Scarface (1983) didn't do sufficient justice to the dire living conditions of newly-arrived Cubans in Florida. 30+ years later, Cuban Americans are known a lot more for great music and the third-best sandwiches in the lower 48 than for crime-ridden encampments and Castro's nasty empty-the-prisons-and-put-'em-boats prank. I don't have the polling data, but I'd put money on the likelihood that a majority of Americans would have a favorable view of the US accepting Cuban refugees in retrospect.
Indeed, I suspect that the historical refugee crises most survey respondents would regret are the ones we turned away. How many European Jews might we have spared the grisliest of fates if we'd have opened the shores in 1939? What if in 1994 we'd have airlifted ethnic Tutsi here? It is indeed better to regret something you have done than to regret something you haven't done, particularly when the latter is soaked in the blood of the innocent.
So up close, the challenges of accepting loads and loads of refugees look insurmountable. From a distance, they seem petty compared to the horrors of the alternatives. Which perspective is more accurate? Which is more useful? Which is better for ourselves and our humanity?
Fleeing violence is not nor has ever been euvoluntary. Heed well the type and severity of the ex post regret incurred when considering the sort of response you favor.