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The new pay-go rules will require that most spending increases or tax cuts be “paid for” elsewhere in the budget by tax increases or cuts to other programs. If the rules are broken, automatic cuts would take effect. The rules would become part of the law, replacing the more-lax chamber rules Congress has imposed on itself, but often waived or evaded when a crunch-time vote came.

Earlier this week, the Senate rejected a bipartisan proposal to create a debt commission, which would have been tasked with proposing a package of reforms to reduce the huge debt level. The proposal would have required Congress to vote on the package as a whole, in theory making it easier to swallow spending cuts and tax increases together.

After that vote failed, Mr. Obama said he would create a commission by executive order to try to recommend solutions. But that panel would not have the force of law to compel Congress to vote on the recommendations.