Strikingly, Mr. Rubio’s principles did not sound that different from proposals for an immigration overhaul by Mr. Obama, Democratic leaders and a handful of other Republicans. Aside from work under way at the White House on legislation, a bipartisan group of Senators has been meeting to draft a bill.

Where Mr. Rubio differed significantly with Democrats was on the legal pathway illegal immigrants would follow, with him proposing a long and indirect course before some of those immigrants could apply to become American citizens.

In a telephone interview, Mr. Rubio said a starting point for his plan was recognizing that the current immigration system was “burdensome, bureaucratic, difficult to navigate and sometimes it just doesn’t work.”

Mr. Rubio said he would seek to reorient the visa system to bring in more educated immigrants with skills in technology and science. As for the estimated 11 million illegal immigrants in the country, Mr. Rubio said, “We have to understand these folks are here to stay.” He added that most of them had not committed serious or violent crimes.