Harry Enten notes that Rubio has become less popular as he has become better-known nationally:

It’s not clear why Rubio has fallen. The decline in his popularity among adults corresponds almost perfectly with his push for immigration reform; his largest drop occurred in June as the Senate was debating comprehensive changes to U.S. policy. I wouldn’t argue that pushing for immigration reform made Rubio unpopular, but it did give him a lot of press. FiveThirtyEight has previously said that Rubio’s ideology ranks as quite conservative. It’s possible that Americans learned more about Rubio than just his views on immigration during that period.

I suspect that Rubio’s favorability has dropped for a few reasons. Following years of being oversold and built up as the walking embodiment of the solution to the GOP’s electoral woes, Rubio’s performance in the Senate in the last two years hasn’t lived up to the hype. Giddy Republicans used to refer to him as the “Republican Obama” and the key to winning a larger share of the Hispanic vote. No one says that anymore now that reality has set in. Many movement conservatives and Tea Party activists that initially rallied to him as one of their own became disenchanted with his immigration maneuvering. Then when he tried to retreat from the Senate immigration bill, he disappointed the bill’s supporters among party elites and “centrist” pundits. Hawks that used to find any excuse to promote him as a possible presidential or VP candidate discovered that his foreign policy speeches were underwhelming and vague, and many non-hawks found reasons in those same speeches to oppose him. Moderates and “centrists” that wanted to celebrate Rubio as a model of bipartisanship because of his support for the Senate immigration bill were then dismayed to watch as he hurriedly abandoned his earlier position. They then became even more disillusioned with him as he desperately tacked back to the right on any and every issue to repair the damage he had done to himself with conservatives. In short, Rubio has managed to annoy or disappoint many of his would-be supporters and admirers while antagonizing many others, and he did so under fairly close scrutiny from the national media, so it is not that surprising that he is viewed much less favorably than he used to be.

Immigration happened to be the main issue involved in most of these reactions, but it was really Rubio’s clueless handling of the politics of the issue that generated so much of the negative coverage he received over the last year and a half. My guess is that it was this negative coverage that has dragged his favorability down. When most people talked about Rubio back in 2011 and 2012, the coverage was generally positive and speculation about his political future was very favorable. This reached its apogee after Romney’s defeat when party leaders and some pundits were eager to “fix” the party’s weakness with Hispanic voters, and Rubio was identified as an ideal candidate to do just that. Ever since then, the story has been one of Rubio’s collapsing support among rank-and-file Republicans and the disappearance of the enthusiasm for his presidential aspirations just as he has started to express more interest in running. This isn’t entirely Rubio’s fault. He was ill-served by the early waves of unearned hero-worship and absurd boosterism during his first two years in office, and he has suffered from the party’s bad habit of over-exposing and over-promoting its newest national political talent.