The administration's warning of dire economic consequences for failing to increase the debt ceiling has not gained traction with the American public, as an overwhelming majority opposes the increase, according to a new poll.

Of those surveyed in a Reuters/Ipsos poll, 71 percent opposed increasing the borrowing authority. Only 18 percent support the increase.

The revelation could embolden some Republican critics of an increase to the $14.1 trillion debt ceiling, and adds another layer of complexity to what is already shaping up to be one of the first major political disputes in the new Congress.

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Treasury Secretary Timothy Geithner warned lawmakers on Jan. 6 that if the debt ceiling is not raised by this spring, there will be "catastrophic economic consequences" both in America and across the globe. While some Republicans leaders have acknowledged that the ceiling must be raised to avoid a default on U.S. debt, the GOP is still looking to obtain promises of serious spending cuts in exchange for their support of the boost.

Meanwhile, House Democrats are indicating that since the GOP has taken the control of the House, it is their responsibility to pull together the votes to get it passed.

Congress most recently increased the debt limit in February, boosting it to $14.29 trillion. Geithner said the current outstanding debt of the government is $13.95 trillion, and the $335 billion in remaining extra space will be exhausted sometime between the end of March and May 16, depending on various factors.

The same poll also indicates that while the GOP has vowed to cut spending, finding ones that enjoy broad public support could be a challenge.

Just 24 percent said the country should cut back on education spending, while 21 percent back cuts to law enforcement.

A slim 51 percent majority of those polled backed cuts to military spending, and slightly less than half — 45 percent — wanted to see cuts in environmental enforcement.

If the GOP wants to cut funding for financial regulators like the Securities and Exchange Commission, they would enjoy a small majority of support; 53 percent supported cuts in the budget of those regulators, even as their responsibilities have substantially increased after the enactment of the Dodd-Frank financial reform law.

The most popular cuts among those polled were reductions in foreign aid and tax collection — 73 percent and 65 percent support, respectively.