Is there an American term for a group of elitist schools, similar to the abbreviation “Oxbridge”?

I saw the word, ‘Oxbridge’, a portmanteau of Oxford and Cambridge, in a comment to a question asking for a better word for ‘invigilator’:

Whereas the situation is reversed in the UK, and one in a thousand would recognize proctor -- although even the one in a thousand would be the one who went to Oxbridge and would give it a different meaning altogether.

We have the abbreviation “東大一ツ橋” (Todaihitotsubashi) combining the names of Tokyo University and Hitotsubashi University, both national universities, as a symbolic phrase of elitist schools, though I don’t know why Hitotsubashi University singly skewed to economics was paired to Tokyo University out of 783 universities and colleges (in 2012) in Japan.

In the sports area, we have the word “早慶” (Sohkei), an abbreviated combination of Waseda University and Keio University, both private universities excelling in baseball, rugby, soccer and many other sports, as well as in academic achievement.

Is there an American counterpart of “Oxbridge”, “Sohkei” and “Todaihitotsubashi,” or does “Yale-Harvard” suffice?

I'm going to omit any caveats and disclaimers, and say that yes, there is an American equivalent of Oxbridge, and it's ivy league. Yes, there are elite colleges in the US that are not traditionally part of the Ivy League, but they can still be described as ivy league (lowercase/adjectival form); and the US is a larger place than the UK (or Japan, for that matter), so it stands to reason that our equivalent of Oxbridge would include a larger group of institutions.

If you really want to restrict your expression to two institutions, that would be Harvard/Yale, which doesn't really lend itself to a portmanteau word. (Haryale? Yalevard? You see the problem.)

"Oxbridge" is well-known across the entire world, but we do also have Redbrick universities.

Note that "Redbrick" was originally a somewhat derogatory term distinguishing six "newer" universities from the seven ancient universities which were all established several centuries earlier. But today many people use "Redbrick" for any of the top dozen or more British universities.

Per comments, there's no direct US equivalent to Oxbridge, partly because it's not so easy to agree on the two and only two top universities (although as John Lawler says, Harvard/Yale must be a strong contender historically speaking). The nearest equivalent is probably...

Ivy League - the name generally applied to eight universities (Brown, Columbia, Cornell, Dartmouth, Harvard, Pennsylvania, Princeton, and Yale) that over the years have had common interests in scholarship as well as in athletics.

Stanley Woodward, New York Herald Tribune sports writer, coined the phrase in the early thirties.

Obviously "Oxbridge" specifically represents the top two in the UK, and I don't think anyone would refer to either Oxford or Cambridge as a Redbrick. But to Brits at least, Ivy League usually means something pretty much equivalent to Oxbridge plus the Redbricks.