No, @EricTrump is not correct, and neither are you.
Let me explain.
First of all, that particular JFK line you're invoking?
It was used most famously in a speech he gave in June 1963 in Frankfurt, in which he called for strengthening NATO, promoted free trade and denounced the use of protective tariffs. http://www.copperas.com/jfk/paulsk.htm
But in a broader sense, is the Democratic Party still the party of JFK?
Well, let's ask the man himself. Here he is in 1960, accepting the nomination of the Liberal Party in New York and, as he did, explaining "why I consider myself to be a liberal." https://www.youtube.com/watch?v=O3oY93doosg …
First, as he noted in that speech, a key tenet of JFK's liberalism was the separation of church and state, a particularly important issue for him as the first Catholic president.
He expressed that clearly in the 1960 campaign in an earlier address:
JFK believed that religious minorities (like Catholics at the time) should be free to practice their own faiths as they saw fit.
Here's his response to the Supreme Court's 1962 decision banning state-directed prayers in public schools:
Second, JFK believed in elevating marginalized groups -- women, racial minorities and immigrants.
Kennedy was an early proponent of feminism.
He established a Presidential Commission on the Status of Women (below), called for paid maternity leave and child care facilities for working women, and secured passage of the Equal Pay Act of 1963. https://www.youtube.com/watch?v=ZOO4X8XZw7w …
Likewise, Kennedy became -- after some initial inaction -- a champion of voting rights and civil rights for racial minorities as well.
Here's the speech he made after Birmingham in June 1963, introducing what would become the Civil Rights Act of 1964. https://www.youtube.com/watch?v=7BEhKgoA86U …
JFK was, after all, the president who coined the phrase "affirmative action."
And, likewise, as a descendant of immigrants, JFK was also an outspoken champion of immigration.
America, as he said in this 1963 speech to the Anti-Defamation League, was "a nation of immigrants." https://www.youtube.com/watch?v=ewk_9wQVVz4 …
Third, in addition to these beliefs, JFK was a proponent of strong government programs to promote welfare.
He promoted expanding Social Security and called for what would become Medicare in this speech in Madison Square Garden in May 1962.
Watch this: https://www.youtube.com/watch?v=VXUJErr_vfo …
(On the other side, we should remember, then-actor Ronald Reagan -- on behalf of the American Medical Association -- denounced Kennedy's liberal call for a national health care program as "socialism.") https://www.youtube.com/watch?v=Bejdhs3jGyw …
Speaking of Reagan, some claim JFK's tax cut proposal was a forerunner of Reagan's, but those tax cuts were quite different.
JFK wanted a *demand-side* cut, not a supply-side one. His plan dropped the top bracket from 91% to 65% -- about where @AOC wants to raise it today.
Conservatives back then hated JFK -- see this flyer that the far right distributed in Dallas right before his assassination -- but these days some of them have rewritten that history to try to claim him as one of their own.
It's an argument that doesn't fit with the history.
JFK was a proud liberal who supported separation of church and state, civil rights for racial minorities and women, immigration, big government programs to expand the welfare state, NATO and free trade.
He dismissed protective tariffs and, oh yeah, he stood up to the Russians.
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