There are now fewer people in the United States that see border security as an important and effective way of dealing with immigration. According to a poll released by Gallup, addressing the estimated 11 million undocumented immigrants already inside the U.S. has surpassed border control as a priority.

Both issues are now equally important, with 43 percent of Americans favoring border security, and 44 percent wanting to focus on a plan for existing immigrants, the poll shows.

The shift has occurred mainly over the last year, but a desire to address the nation's millions of undocumented immigrants has been replacing the image of a perpetually broken fence since 2011. Support for securing U.S. borders reached its peak in 2011, with 53 percent of Americans favoring that approach. That was during the heat of the 2012 Republican presidential primary, when, for example, Herman Cain proposed an electrified border fence with moats and alligators. The percentage of those saying border security should be the top priority of immigration legislation declined to 41 percent in mid-2013, before ticking up slightly to 46 percent now. 

Some Republicans still stress border control as the best way to proceed with immigration reform. Earlier this month, Wisconsin Rep. Paul Ryan spoke about a GOP plan that puts border security first, and does not include a way for immigrants to achieve citizenship, calling it a "security force first, non-amnesty approach."

One of the reasons for the shift is that fewer Republicans and Democrats view border security as the favored option for immigration reform. There has also been a 4 percent uptick in the number of Democrats who see dealing with immigrants already in the U.S. as the best option.

On Friday, President Barack Obama told Univision Radio that immigration reform will pass before he leaves office in January 2017, adding that the best approach is to put pressure on Republicans who have so far refused a deal. 

Figures show that Americans are becoming more positive towards immigration. Last July, Gallup found that 72 percent of those asked consider immigration to be a good thing from the U.S., compared to 57 percent in 2010.