It is getting close to “crunch time” in the debate over raising the debt ceiling. Much of the debate continues to focus on whether Republicans will accept tax hikes as part of the package, and how big the debt-reduction package will be. All sorts of numbers are being tossed out: $4 trillion over twelve years? $6 trillion over ten years? $3 trillion over two years?

But focusing on dollars — even trillions of dollars — may be setting Republicans up for a fall.

After all, we’ve heard promises of spending cuts before. Remember the deal over the continuing resolution that kept the government open back in April? That deal was supposed to include $61 billion in spending cuts, but, in reality, it was crammed full of gimmicks such as counting savings from spending that hadn’t occurred in the previous year or not funding programs that actually didn’t exist. In the end, the actual reduction in spending was less than $8 billion.

And President Obama, in his most recent budget proposal, counted interest savings and the elimination of tax breaks (“spending in the tax code”) as reductions in spending. They might show up that way on a balance sheet, but that sort of budget cutting does very little to reduce the size and burden of government — which is what this debate should really be about.

Republicans must also ask when those spending cuts will occur and how will they be enforced. Budget history is flush with promises of cuts some day in the future — but some day never actually comes. This is especially true when budget savings are anticipated not from actually eliminating programs, but from making government “more efficient.” For example, the Obama administration claims that the health-care-reform law will ultimately save some $500 billion in Medicare spending. But even Medicare’s own actuaries don’t believe those savings will ever occur.

Now, the administration is reportedly offering another $340 billion in Medicare and Medicaid cuts as part of a budget deal. But because the administration continues to resist any changes in the structure of the program, those savings are likely to be as ephemeral as the Obamacare cuts.

And speaking of those Obamacare cuts, the health-care law “double counted” those Medicare savings by routing them through the so-called Medicare Trust Fund. This type of “trust-fund accounting” allowed the administration to “extend the life of Medicare” and reduce the program’s unfunded liabilities, even as the savings were actually spent elsewhere. Will the debt-ceiling deal include similar smoke and mirrors?

That is why Republicans should not get hung up on seeking any particular amount of spending cuts. The dollar amount matters far less than getting the structural and institutional changes that will actually bring down the size, cost, and intrusiveness of government in the future.

Republicans should push hard for a balanced-budget amendment to the Constitution — and not one that simply requires a balanced budget, but one that includes meaningful spending limitations. If they can’t get the two-thirds vote that such an amendment would require, they should at least insist on a statutory spending cap. Republicans should also insist on fundamental structural changes to Medicare, Medicaid, and Social Security.

In the end, this is not really a debate about budgeting or the size of the national debt. It is a debate about whether we will have a limited constitutional government or a European-style social democracy. Winning that debate will not be a question of whether there is an agreement to cut $2 trillion over ten years rather than $1.5 trillion. If Republicans get an extra $500 billion in cuts on paper, but leave the structures of big government in place, they will find out down the road that nothing has really changed.