WASHINGTON

OUR paralyzed government is lurching toward an agonizing series of budget deadlines. Without some kind of deal, nearly $1 trillion in across-the-board spending cuts will kick in on March 1, the federal government could shut down on March 27, and the nation could default on its debts in May. On Tuesday, President Obama called the looming cuts, known as the sequester, a “meat-cleaver approach” as he urged Republicans to accede to higher taxes.

The search for an elusive grand bargain — more taxes, fewer benefits — may be blinding us to the potential for incremental progress. The two parties fundamentally disagree over the future of our welfare state, but there may be space for common ground.

Democrats want to close the budget gap by having the government lean more heavily on the wealthy, while Republicans want to close it by having the government spend less money. Both sides should agree at least to spend less money on the wealthy — via means testing. It may surprise some Americans to learn that the United States spends quite a lot on the affluent, especially through the entitlement programs at the heart of the budget fight: Social Security and Medicare. Both programs move money from relatively poorer young people to relatively richer old people, and they are growing ever more expensive. Means-testing — allocating benefits according to need — might offer both sides a way out.

The approach would require agreement on two principles. First, give less to the wealthy rather than take more from them. For Medicare, such means testing would mean giving prosperous older people fewer benefits rather than charging them higher premiums for the same benefits other elderly Americans get. Charging wealthy older Americans more, and then giving money back to them through an expensive and inefficient benefit, makes no sense. The goal should be to better target public benefits to those who need them.