After looking at the piece (by Robert Kagan) my sense is that Venusian is here intended as the opposite of Martial (in the sense of warlike). Where President George W. Bush displeased European opinion by being far too eager for war, his successor has been notably less eager, and that is the change Mr. Kagan seems to be talking about.
The two planets are opposite not only in the sense that their astrological symbols double as symbols for the two sexes (and Mr. Kagan may well be subtly calling Mr. Obama what Mr. Trump less subtly called Mr. Cruz a week ago), but also in ruling or co-ruling opposite humors: Mars the yellow bile, hot and dry and associated with belligerence, irascibility, and anger; and Venus the phlegm, cold and moist and associated with placidity. (These planets share the astrological rule of these humors with the sun and moon respectively.)
My source here is John W. Draper, The Humors and Shakespeare’s Characters (Durham, NC: Duke U.P., 1945; rpt. New York: AMS Press, 1965).
I do not think the term refers here to runaway greenhouse effect, though the planet Venus is often cited as a cautionary example of that.
As cobaltduck has astutely noted in a comment hereupon, the opposition of these two planets in relation to sex and/or gender was given renewed currency by John Gray’s 1992 pop-psych bestseller Men Are from Mars, Women Are from Venus.