President Obama may not be on the ballot on Tuesday, but his re-election effort faces some key tests as voters go to the polls in important 2012 states like Ohio.

With the fate of collecting bargaining rights for public employees on the ballot in that key battleground, this is a major test to see if the president's vaunted get-out-the-vote operation from 2008 is still a well-oiled machine ready for 2012.

That's why officials from organized labor and the Obama re-elect team have been on the ground in Ohio trying to turn out the vote on the ground. Back at the White House, Press Secretary Jay Carney was adamant about where the president stands on the measure.

"Let me be very clear: The president does not support the ballot initiative in Ohio that would strip away fundamental collective bargaining rights," Carney said at his daily briefing Monday.

But the president himself has not spoken out on the matter since April, when an Ohio reporter asked him about it. "Let's certainly not blame public employees for a financial crisis that they had nothing to do with," Obama said. "And let's not use this as an excuse to erode their bargaining rights."

The low profile is a far cry from the aggressive approach Obama suggested he would take in the White House back in the 2008 campaign. "I've walked picket lines before," he told one audience in 2007. "I've got some comfortable shoes at home."

Carney said the president has not spoken on the issue recently only because White House reporters have not asked him at recent news conferences. But a senior Democratic official privately said there may be another explanation for the silence.

Polls show organized labor is leading on the ballot initiative by double-digit percentage points, so unions didn't really need the president's help -- and may have been leery of Obama riling up conservatives if he got too heavily involved in the effort.

"Labor didn't want it to be about the president," said the senior Democratic official, who asked for anonymity to discuss private deliberations. The official noted union officials are ahead by a wide margin. "They were afraid (Obama involvement) could rally the opposition."

At stake is Issue Two, whether or not to keep a new state law restricting collective bargaining rights for Ohio's more than 300,000 thousands workers who belong to public employee unions, including teachers, police officers, and firefighters.

Republican Gov. John Kasich is pushing to keep the law with a "yes" vote on the referendum because he says bloated local government is killing job creation in his state, where high unemployment is putting Obama's hold on its electoral votes in jeopardy.

"If local communities can't control their costs and keep raising taxes, it becomes an impediment particularly for small businesses to be there," Kasich told Fox News.

The issue tripped up Republican presidential candidate Mitt Romney last month, when he didn't take a stand on Issue Two or Issue Three, another ballot initiative, aimed at preventing the president's health care law from taking effect in Ohio.

"I am not terribly familiar with the two ballot initiatives," Romney said last month.

Romney quickly apologized and said he backs Kasich. But he's now facing more heat over whether or not he supports what's known as the "personhood" amendment on Mississippi's ballot on Tuesday.

The amendment would define a fertilized egg as a legal "person," and the Democratic National Committee has been suggesting in a letter to supporters and an ad that Romney is an extremist for backing the amendment.

Democrats are particularly jumping on the issue now that other Republicans who support the measure, like outgoing Gov. Haley Barbour, have said they support the measure but acknowledge it may go too far.

But advisers to Romney stress he never got behind the Mississippi measure. They accuse Democrats of just basing their attacks on a hypothetical question the candidate answered about life beginning at conception.

"It's too bad this White House isn't as focused on attacking unemployment as they are in attacking our campaign," Romney spokesman Andrea Saul told Fox News.

The bottom line is that if organized labor is able to win on Issue 2 in Ohio, it may show that the intensity for 2012 is not just on the right -- the left is still fired up as well.

But if organized labor wins that one with the president on the sidelines, it will certainly raise questions about how much enthusiasm there is behind Obama himself in the months ahead.