The already difficult job of the congressional supercommittee tasked with cutting at least $1.2 trillion from the federal deficit got even more difficult last week. The latest complication came in a letter to the committee signed by 33 senators stating they oppose any deal including net tax increases.

Rather than make a deal less possible, the letter could be used as a bargaining chip to get to a “grand bargain” including major spending reductions and somke tax increases to seal the deal.

But if Republicans on the committee intend to stick to the no-higher-taxes plan they could trigger automatic — and deep — cuts across the board, including major cuts to defense spending. Such intransigence could cost Republicans support among independents and moderates, considered the critical voting block in the 2012 election. And by triggering deep cuts to defense spending, the GOP could hurt itself with strong-on-defense conservatives.

The letter from the 33 Republican senators said the supercommittee plan should “balance our budget within 10 years and place entitlements on a path to solvency.” The letter also endorced comprehensive tax reform that lowers rates and promotes growth.

Those are all worthy goals, although the 10-year time frame for a balanced budget might be too aggressive considering that the deficit has been decades in the making. It’s also worth noting that while the stated corporate tax rate in the U.S. is the second-highest in the developed world, the actual tax rates paid by many large corporations is much lower. A complex tax code full of legal tax breaks and loopholes produces a lower tax rate for many, mostly large, multinational companies.

The supercommittee should take advantage of the public support for bold tax reform that includes simplification of the tax code and reduction of loopholes and deductions.

The supercommittee knows that most American realize that the tax code is riddled with loopholes paid for by lobbyists and campaign donations. It’s members also know that most Americans also favor bumping up taxes on the wealthiest among us.

While it’s true that the wealthy pay a large portion of total income taxes, it’s also true that the tax rates on the wealthy are at historically low levels. Returning to the tax rates of the Clinton administration would not be unreasonable, and even a majority of well-to-do Americans support such a move.

The Simpson-Bowles commission on deficit reduction along with other, similar studies have all suggested meaningful deficit reduction is best accomplished with a combination of spending reductions and tax increases. Depending on the group’s political leaning, the relationship of spending cuts to tax increases varies. But all serious proposals recognize that both are needed.

The emphasis should be on spending reductions because recent trends are unsustainable even with higher taxes, but some tax increases should be part of the mix.

Democrats should admit that entitlement spending must be curbed. They should also acknowledge that even major tax increases on the wealthy would not change that fact.

Republicans should press for significant spending reductions, then, to close the deal they should accept increasing taxes on the wealthy to Clinton-era rates. Such a compromise would have the most impact on the deficit, which conservatives claim to care about — and it would be seen as a fair plan, suggesting shared sacrifice.

The supercommittee was created in August because Congress proved unable to addresss the deficit problem. Pressures on the committee are intense, but despite their partisan differences, the 12 members understand what needs to be done — for the good of the county, not for Republicans or Democrats.

Committee members have only a few weeks to prove they are willing and able to put country ahead of party.