It's all in how the quetion in the polls are asked. In many polls, if you look for them, you'll see people clearly contradicting one answer when another is asked.
I don't believe the currently cited Gallup poll represents as much shift in public opinion as is implied.
Here is a cross sampling of many polls over the last year:
http://www.pollingreport.com/immigration.htm
As nearly as I can tell, I think if the questions are phrased to allow the people to fully express their opinions, the majority consensus at this time is:
1) Stop the flood of illegals into the country using any reasonable means.
2) Give those illegals already here a brief amnesty period in which they can go home and come back through legal means.
3) Nobody should be rewarded in any way for breaking our laws or have any advantage over those who have applied to immigrate legally.
4) Immigration quotas should be increased.
5) Immigration policies should be revamped to make immigration less of a nightmare.
6) Those immigrating on a temporary basis should undergo thorough background checks and if they have a criminal record in their home country or in the USA, they should not be admitted.
7) Ditto for those immigrating with the intention of becoming U.S. citizens, and those seeking citizenship should want to be Americans and rooted here.
8) A $10,000 fine to 'buy' admission to the USA gives an unfair advantage to the rich.
9) Nobody in the country illegally should be eligible for any benefits or social sevices other than emergency humanitarian aid prior to deportment.
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--Foxfyre
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I?-
I took the one less traveled by,
And that has made all the difference.