It's the discussion that dominated the Sunday talk shows this weekend as it has dominated New York's political conversation for weeks -- the possibility of Caroline Kennedy being appointed to Hillary Clinton's US Senate seat.

Of course, as JFK's daughter, and the niece of RFK and Ted Kennedy, some are disparaging her famous family name.

Adding fuel to the fire is another person whose name has been mentioned in connection with the seat -- New York Attorney General Andrew Cuomo, who was not only married to Kennedy's cousin, but has a political pedigree of his own.

"In New York, it's a question of whether the daughter of an ex-president or the son of a former governor should be the next senator. What's wrong with this picture?" said Washington Post Columnist George Will.

"The last thing we need is a people magazine celebrity as our US senator. Especially someone who has no experience, who as far as I know has never held a real job," said Congressman Peter King, who has also expressed interest in the seat.

Kennedy has in fact worked for the city school system, heading the Office of Strategic Partnerships, which raises private funds for the public schools. Her former boss, schools chancellor Joel Klein, spoke highly of her on Sunday.

"I also think she'll have the relationships on Capitol Hill to be able to get the work done," said Klein.

Perhaps the loudest criticism is over access.

Over the weekend, a spokesman for Kennedy answered a series of questions about her positions on the issues, questions that were submitted in writing from news outlets and blogs.

Even if she is appointed to the post by Governor Paterson, that's only step one. Kennedy would then have to go through a special election in 2010 to finish Clinton's term, and then re-election in 2012, the beginning of the next six-year cycle.

Many are wondering whether this intensely private woman has the stomach for so much scrutiny.

"If she wants this seat she's going to run for it and she's going to have to face something she's never faced before," said All Things Considered Host Michelle Noris, NPR.