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“Both sides acknowledge there are these loopholes in the code that should go,” he said. “In the context of a smaller deal, identifying one or two for a solution seems reasonable.”

However, even that possible point of agreement isn’t without challenges.

Chris Edwards, editor of DownsizingGovernment.org at the Cato Institute, said the two parties can’t even agree on what constitutes a “loophole” — which means negotiators will have a tough time agreeing on whether to get rid of them.

“That’s a real hurdle — it’s that Democrats’ basic understanding of tax policy is just fundamentally different from Republicans,” Mr. Edwards said.