In keeping with your specific distinction about charges of actively hating America and deliberately working to sabotage and/or undermine American ideals (as opposed to more general mudslinging about the disaster the opponents' ideas will wreak), you would be extremely hard-pressed to find an example of this charge coming from the left against the right. I've linked to a couple of examples below, but really, patriotism and love of country are basically the conservative party's entire schtick, so it doesn't make a lot of sense -- even among the left -- to argue that conservatives hate America.
As far as its novelty goes, it's a relatively new thing, only going back about 50-60 years or so. Most conservatives would point to the 1960's counterculture and the "New Left" as the beginning of the rise of domestic anti-American sentiment, although they would also argue that the seeds were sown during the Progressive era of the 1920's and 1930's. The reason? Communism and the Vietnam War respectively.
From the mid-20th century onwards, the American right has always criticized the left for its casually flirtatious attitude toward Marxist ideology. The New York Times just recently ran a glowing article titled Happy Birthday, Karl Marx. You were right!
During the Progressive Era, many intellectuals on the left were openly supportive of the communist and fascist ideologies (the Frankfurt School and the American Eugenics Society, for example) that were taking hold in Europe and Russia. To be fair, those ideologies were new at the time and the atrocities of Hitler, Stalin, and Mao were not yet known. The Red Scare during the 1950's (after those atrocities became apparent) was merely a reaction (overreaction?) to this marked shift in political philosophy.
However, during the Vietnam War era (and the reaction to the reactionary Red Scare), domestic anti-American movements gained a wide cultural foothold in the form of the Peace movement (hippies), 2nd-wave feminism, radical environmentalism, radical elements of the Civil Rights movement (e.g. Black Panthers), and American anti-impirialism. Many of the criminal acts promulgated by these radical leftist groups would be considered domestic terrorism today, and the ideologies that motivated them can have their roots traced back to Marxist ideology.
Much of that radical leftist streak is still present in modern hard-left political rhetoric in the form of identity politics, "Democratic Socialism", and postmodernism (I use the term here to mean skepticism of the Enlightenment-era philosophies on which America's founding documents are based).
So when the right says that the left hates America, it is this particular set of ideologies they are referring to. In the conservative's view, these ideals bear little resemblance to, and are fundamentally incompatible with, America's founding creed.
More broadly with regard to mudslinging in general, (my opponents will destroy America) there's nothing new or particularly conservative about it. Various ad-hominem attacks on political opponents are as old as the republic itself and by no means limited to either party; only the particular form it takes differs, depending on the time and political climate.
This site mentions some pretty good zingers going all the way back to the 18th century. In the 1796 election, John Adams claimed that Thomas Jefferson was an atheist, wanted to free the slaves, and would start a civil war (he was right about the last two -- but that was considered anti-American back then).
In modern politics, conservatives say liberals hate America, and liberals say conservatives will destroy America. Liberals are communists, conservatives are fascists, and they both hate American values if all the stupid rhetoric is to be believed. To balance out the examples you gave in your question, I submit the examples below of how the left thinks the right hates America:
- The Hill reports that the Tea Party (a conservative group) hates America
- Salon says the right hates America too.
- Joe Biden said during the 2012 elections that Mitt Romney wants to "Put y'all back in chains"
- Many on the left, including Senaror Elizabeth Warren, Senator Bernie Sanders, Congressman Alan Grayson, and others in the media, accused Republicans of wanting people to die during the 2017 Obamacare repeal bill debate in Congress, (hilariously mocked by this video -- well worth the watch!)
- Google Republicans hate (sick people/poor people/brown people/women/etc and you will get more hits than you could possibly read (including this one from Salon which reports this "fact" as scientific research)
- Pretty much any "documentary" from Michael Moore suggests that Republicans will destroy America.
Basically, fearmongering, demagoguery, and negative campaigning are a baked-in component of democracy and have been around since democracy was invented. It is only the particular form it takes that changes from era to era and from party to party.