Last Friday House Majority Leader Eric Cantor sent a memo to Republican colleagues that paid homage to middle class Americans who “do the hard work of setting a budget and then figure out how to balance paying the bills.” But family budgets do not work that way. People make budgets in order to avoid spending more than their available income; they do not decide how much to spend and then figure out how to “balance paying the bills.”

Cantor’s strained analogy to federal budgets highlights the struggle to find a “conservative” rationale for January’s decision by congressional Republicans to support spending half a trillion dollars more than estimated revenue in this fiscal year. Republicans did not solve their problem in February when many voted against debt needed to pay for that spending; it is hardly “conservative” to incur an obligation and then refuse to pay for it with cash or credit.

Cantor’s memo (and a bill that passed the House today) illustrates the GOP’s debt dilemma. The Majority Leader described the need to raise Medicare providers’ reimbursement rate as a “must do” item requiring immediate action. Without legislative relief those fees would drop by 24 percent on April 1. That drop would be required by a ceiling on reimbursements that served as the lynchpin of the bipartisan Balanced Budget Act of 1997. The ceiling was designed to force hard choices about the growth in Medicare spending. Since 2003, Congress has instead routinely chosen to suspend, but not permanently modify, application of the fee cap.

A 24 percent drop on April 1 could prompt some physicians to drop Medicare patients, so House Republicans proposed to offset the cost of a fee increase with a sleight of hand: they will “cut” Medicare in 2024, the last year of a ten-year window used to calculate the impact of legislation on total debt. Of course, everyone realizes that a “cut” in 2024 can easily be restored by some future Congress, just like was done today with the “cut” in Medicare fees.

The House Republicans had other alternatives to incurring greater debt. Higher fees to providers could be financed with higher Medicare payroll taxes and premiums. After all, the portion of Medicare paid for with dedicated revenues fell from 73 percent in 2000 to 53 percent in 2010, and raising taxes to reduce Medicare borrowing would generate more pressure to restrain the program’s cost. But that approach would compel the GOP to acknowledge the gap between its spending and tax policies.

Republicans could have proposed cuts in Medicare services in order to offset the cost of paying reasonable fees to physicians. Yet, Cantor’s memo to Republicans did not even hint at that alternative, for a well-understood reason. As Alan Greenspan noted in The Age of Turbulence, John Boehner rationalized the 2003 unfunded expansion of Medicare (at a time when he was the chair of the House Republican Policy Committee) by writing that “the American people did not want a major reduction in government.”

Years ago President George W. Bush used humor to gloss over the conflict between his tax and spending policies. He began his 2001 State of the Union address by requesting higher spending and vowing to reduce debt by $2 trillion in order to protect “our children and grandchildren.” He then quoted Yogi Berra—“when you come to a fork in the road, take it”—and asked for a massive tax cut. Ever since, spending has followed one fork and tax policy has followed another.

President Reagan said that “there are no easy answers but there are simple answers.” So long as the Republican leaders complain about rising entitlements and debt, and use debt to ease the growth in Medicare, they will not be able to embrace the simple answer of a balanced budget. Instead they will—as Cantor says—set a budget and “figure out how to balance paying the bills.”

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Bill White , chairman of Lazard Houston, is the author of America's Fiscal Constitution: Its Triumph and Collapse. He was the mayor of Houston from 2004 to 2010 and the U.S. deputy secretary of energy from 1993 to 1995.