Voters have long favored President Obama over Mitt Romney for handling terrorism and advancing the interests of the middle class. Romney, however, has consistently enjoyed a wide advantage on only one issue: the nation’s gaping budget deficit.

But now the Republican presidential nominee, who tried to bolster his deficit credentials by picking a budget hawk, Rep. Paul Ryan, as his running mate, is at a significant risk of losing the edge on the policy area that voters have trusted him most on. It is an issue that dominated the political debate last year and will again immediately after the election.

Two recent national polls show a narrow gap between Romney and Obama on the deficit. Romney seems to have lost his advantage after weeks of being pilloried by Democrats for his policies, which they claim would cut taxes on the rich, raise taxes on the middle class and cost seniors more for health care.

Conservatives and independent analysts, meanwhile, have been increasingly questioning whether Romney’s proposals are detailed enough to justify their claims.

The cumulative effect seems to be taking a toll on Romney’s reputation as someone who will fix the nation’s debt burden. Just as voters are beginning to pay close attention to the election, the fiscal problems of Europe are dominating the headlines, and the end-of-year “fiscal cliff,” with a recession-inducing series of tax hikes and spending cuts, comes into focus.

Obama and Romney each claim to have a plan that will the cut the debt by about $4 trillion over the next decade, which would be roughly enough to stabilize the size of the debt compared with the overall economy.

To close the gap, Obama calls for tax hikes on the wealthy, spending cuts and modest changes to entitlements. Romney relies solely on spending reductions.

Although Americans support deficit reduction, polls show they do not favor cuts in entitlement programs such as Medicare. They do, however, support raising tax rates on the wealthy to close the deficit .

“Even if they agree with the approach he says wants to take [to reduce the deficit], they don’t believe he’s going to follow through,” said Jonathan Burks, deputy policy director of Romney’s campaign.

Critics point out that Obama has far from a perfect record on the debt. The country added about $4 trillion to its debt during Obama’s term, in part because of the recession, and he failed to live up to his promise to halve the deficit. He also didn’t fully embrace the report of the Simpson-Bowles deficit-reduction commission he created, a frustration for many of the president’s supporters in the business community.

“The president would attract more CEOs if he’d adopt Simpson-Bowles,” said Marc Benioff, an Obama campaign co-chairman and chief executive of “I’ve told the president that I felt that is the right plan. He should reconsider his position.”

The president last summer sought and failed to strike a “grand bargain” to trim $4 trillion from the federal debt in negotiations, an achievement that his political advisers have said would have provided a major boon to his reelection campaign.

Romney has tried to capi­tal­ize on Obama’s weaknesses, largely embracing the House Republicans’ aggressive plan to cut spending and citing his record as a businessman who knows how to balance a budget.

For much of the year, the strategy seemed to work. The former Massachusetts governor enjoyed leads of eight to 17 percentage points over Obama in Washington Post-ABC News polls on the deficit issue.

“It’s all about you don’t spend more than you make,” said Dennis Miller, 62, a retired educator and undecided voter in Loveland, Colo. On the deficit, “Romney has my support because he has more of a business background and understands budgets and understands business, and I trust his instinct in that area more than I do Obama’s.”

But now Romney’s advantage is slipping. In the most recent Post-ABC poll, conducted after the conventions, the difference on trust to handle the deficit narrowed to 47 percent for Romney and 44 percent for Obama, within the poll’s margin of error. A CNN poll conducted during the convention had a similar finding.

Several factors seem to be behind Romney’s losing ground. Democrats have lampooned him for policies they say would raise costs for seniors seeking health care. And they say that he hasn’t been forthright about how his proposal to cut tax rates for the wealthy would either require higher tax revenue from the middle class or add to the deficit.

Analyses by nonpartisan groups such as the Kaiser Family Foundation and the Tax Policy Center have bolstered the claims.

I don’t think he has taken seriously the challenges that the country faces in figuring what he wants to do. He thinks he can be all things to all people,” said James Kvaal, the Obama campaign’s policy director. “He thinks he can simultaneously appeal to people who want a tax cut and appeal to people who are budget hawks.”

Romney has said he would reduce tax rates to spur economic growth and completely make up for the lost revenue by eliminating deductions. He has repeatedly refused, however, to list which deductions he would strike, leaving many analysts to say that what he proposes is a mathematical stretch, if not an impossibility.

Romney also has faced criticism from leading lights of the Republican Party and prominent conservative publications such as the Wall Street Journal editorial page for his policy vagueness.

“The assertion that you are more competent than President Obama strikes many people as merely that — an assertion. It would be supported by your speaking in more detail about a range of financial issues,” conservative commenator Peter Hansen wrote last week in the Weekly Standard.

Alan D. Viard, an economist at the conservative American Enterprise Institute, said Romney has muddied his message in recent weeks. Romney has proposed overhauling the program to offer vouchers to seniors to buy health insurance on the open market in order to save costs, a proposal Obama has said would put a bigger burden on seniors.

But Romney shot back, saying that to pass Obama’s health insurance law in 2010, the president cut $700 billion in future Medicare spending. Romney pledged to restore it.

“To see a Republican ticket advocating increasing the deficit by increasing spending on an entitlement is not something you want to see,” Viard said. “Medicare is popular. The debate in the campaign over Medicare has almost changed over who will spend the most money.”