September 8, 2012, 4:46 p.m. ET

VIRGINIA BEACH, Va. – Mitt Romney seized on the possibility of defense cuts taking effect soon as he tried to woo voters in a once-red state that's heavily tied to the military. He also reminded voters that Democrats had removed a reference to God from their party platform before restoring it later.

In a state with relatively low unemployment – 5.9% in July – the Romney campaign has pounced on the possibility of defense cuts as one component of a strategy to win over the working class, white voters and move Virginia to Mr. Romney's column. In 2008, President Barack Obama became the first Democratic presidential candidate since the 1960s to win the state.

Virginia, home to the Pentagon, defense contractors and military bases, could face a blow to its economy if Congress doesn't act to prevent a $500 billion cut to the Pentagon's budget in January.

"It's unthinkable to Virginia, to our employment needs, but it's also unthinkable to the ability and the commitment of America to maintain our liberty," Mr. Romney said at a rally at the Military Aviation Museum here Saturday.

Mr. Romney sought to pin the blame for the cuts on the White House, noting that journalist Bob Woodward's new book says the idea originated there. "It was their idea," Mr. Romney said.

In a fight that nearly shut down the federal government last year, Republicans refused to raise the federal borrowing limit without deficit reduction measures. When the two parties couldn't agree on how to cut the deficit, they created a bipartisan congressional committee to come up with a plan. They also agreed that if the panel failed -- which it did -- then automatic spending reductions would kick in.

To ensure both sides of the aisle would feel the pain from those cuts, the agreement included sharp defense-spending reductions, as well as cuts to programs that Democrats wanted to protect.

Mr. Obama and most Democrats want tax increases on high-earning taxpayers to be part of any deficit-reduction plan, while Republicans want only spending cuts. "Mitt Romney knows that the only thing standing in the way of preventing the automatic defense cuts he decried today is the refusal of congressional Republicans, led by his running mate, Paul Ryan, to ask for another dime from millionaires and billionaires," said Lis Smith, a spokeswoman for the Obama campaign. "Mitt Romney should call on Congressman Ryan and his Republican colleagues in Congress to end this gridlock and prevent these cuts."

Mr. Ryan, a Wisconsin congressman who Mr. Romney placed on the GOP ticket, voted for the legislation that created the spending cuts, also known as sequestration. He proposed an alternative option in his own budget in the House, which would have cut other domestic spending to preserve military spending.

"I will not cut our military. I will maintain our military commitment," said Mr. Romney, whose has proposed a roughly $2 trillion increase in defense spending over the next decade but has offered few details about how he would pay for it. "We must have a military second to none, so strong no one would ever think of testing it."

Facing a narrow road to victory in the fall, the Romney campaign is hoping to flip Virginia red this year by talking up the state's military underpinning and firing up social conservatives.

In his comments Saturday, Mr. Romney took a dig at Democrats for stripping a mention of God from their party platform and then, after controversy ensued, adding it back in during last week's national convention. Mr. Romney appeared with Pat Robertson, the conservative TV evangelist whose political commentary has spurred several controversies.

At one point, Mr. Romney insinuated that the president would remove any reference of God from American currency, a stance Mr. Obama has never advocated.

"I will not take God . . . out of our platform," Mr. Romney said. "I will not take God off our coins. And I will not take God out of my heart."

The Obama campaign said Mr. Romney was "associating with some of the most strident and divisive voices in the Republican Party."

—Laura Meckler contributed to this article.—Sara Murray covers the 2012 presidential campaign. Follow her on Twitter @SaraMurray

Write to Sara Murray at sara.murray@wsj.com