They aren't trying to make a Constitutional argument that Obama can't nominate someone, but that they are making an argument that they have the right to block someone. If the confirmation period takes as long as Bork-Ginsburg-Kennedy it will carry out until after the election, and if Hillary or Bernie wins they will quickly confirm who Obama has as the current nominee, yet if a Republican wins they will hold out.
Publicity and a politician giving something publicity are a little different, and in most cases politicians should only give something like this publicity if the offender was breaking the law. And yes, Dayton still needs to improve his image.
Yeah, it's really dumb, but Dayton should not have drawn attention to the issue as it makes him look like he is trying to politicize it to improve his image.
Cruz's views are something between evangelical, libertarian, TEA partier, and anti-establishment. Trump's are between birther, truther, neo-nazi, and medical quack.