LAKE BUENA VISTA, Fla. — Mitt Romney offered a family-friendly approach to the nation’s immigration woes in his first general-election outreach to Latino voters, but the modest steps that he sketched underscored the political pull-and-tug the issue has become for the Republican presidential candidate.

His more moderate tone Thursday on a number of side issues contrasted with the tougher stance he took during the GOP primaries. Yet in outlining the path he would take as president, he declined to take on the larger and thornier problem of the 11 million men, women and children already in the country illegally.