Despite polls like these I HIGHLY doubt that immigration will be a losing cause for republicans.
In Europe, during the last two decades, anti-immigration has been nothing but a winning cause for the right. Basically, if immigration has been the hot topic in an election, then the right wingers have won. For years, people assumed that this was a European thing and that the same couldn't happen in the US, with the US essentially being an immigrant country AND the US only having very few muslim immigrants, but 2016 pretty much proved that notion wrong. There is a VERY big audience for scape-goat politics (whether the target are muslims, mexicans, africans, jews or any other minority for the right - or even billionaires, wall street and bankers for the left) and white identity politics, particularly amongst the working class.
So why do I doubt the polls? Because the polls have been similar here in Denmark for decades. Just looking at the polls would not tell you that there is still an immense appetite for anti-immigration measures, but there is. Social desirability bias explains some of this, but another more important thing is that VERY FEW PEOPLE will get motivated to go to vote based on the idea that minorities are being treated unfairly, while a HUGE NUMBER OF PEOPLE will go to vote based on getting tough on immigration. So it really doesn't matter if some draconian anti-immigration bill only has 30% support if those 30% vote based on that bill and the 70% who are against it, does not.