Just hours after Caroline Kennedy ended her bid for Hillary Clinton’s Senate seat Thursday, Mayor Bloomberg was once again clashing – loudly and publicly – with Gov. Paterson.

Coincidence?

Hardly.

After all, jousting between Big Apple mayors and New York state governors is the natural state of affairs – not the other way around.

So expect more fireworks – particularly given the fiscal squeeze both men face.

On Thursday, Mayor Mike blasted the governor’s plan to cut as much as $1.6 billion in state aid to the city.

“I understand all localities are being asked to take a bitter pill,” Hizzoner complained, referring to the proposed cut. “I don’t think it’s fair that New York City is being asked to swallow an entire bottle.”

Of course, every special interest is saying exactly the same thing: Paterson, they insist, needs to make deep cuts – to the other guys’ funding.

The mayor even warned, “We have got down to a level at this point where all the cuts from now on will be in the classroom.”

But wait a minute.

Is he suggesting that the city has yet to make any trims in core educational spending – that all funding rollbacks so far (assuming there were any) have been made outside the classroom?

That would truly be odd, given the supposed severity of the fiscal crunch.

As is, for that matter, Hizzoner’s apparent belief that New York can weather the economic downturn without scaling back the public workforce: Insufficient state aid, Mayor Mike said, is a recipe for – sit tight – layoffs.

Uh, hello?

The whole world is engaged in layoffs these days.

New York state has lost 100,000 private-sector jobs in the past two months.

Even Microsoft – which has never laid off anyone – announced (on the same day Bloomberg was whining) that it would soon eliminate as many as 5,000 of its jobs.

Can public employees be spared?

Should they be spared?

Now, for the past few weeks, Bloomberg may have felt he needed to mute his criticism of Paterson’s budget proposals – because he wanted the gov to tap Kennedy for Clinton’s Senate seat.

But all that’s history now.

It’s back to warfare-as-usual.

Remember, New York City mayors are concerned primarily with the city’s interests; governors worry about the entire state. Their goals and concerns, of necessity, often clash. Consider:

n Gov. Mario Cuomo and Mayor Ed Koch battled – and both were Democrats.

n Gov. George Pataki clashed with Mayor Rudy Giuliani; both were Republicans.

It would be strange indeed, particularly given their tight budgets, if Gov. Paterson and Mayor Bloomberg didn’t likewise go at it – the former being a Democrat, the latter, a who-knows-what these days.

So stay tuned.

If nothing else, it should make for good entertainment.