Pronunciation of "Obama" as "Obamar"

Solution 1:

This is an example of an intrusive R, which people who speak non-rhotic dialects (i.e., they tend to drop the r sounds at the ends of words) often insert between a word that ends with a vowel and another word that begins with a vowel. This avoids the need for a glottal stop, which can be a bit awkward to pronounce. Interestingly, the intrusive R happens even when the first word doesn't end in the letter R, as is the case here.

People who don't use the intrusive R typically insert a glottal stop ("Obamaʔis") or simply elide the first word straight into the second ("Obamaaais").