WASHINGTON — President Barack Obama is predicting congressional approval of the tax-cutting compromise he has reached with Republican leaders, but he’s not ruling out that unhappy Democrats will make some changes.

In an interview today, Obama said that despite a rebellion by many Democrats against his tax deal, it will pass because “nobody — Democrat or Republican — wants to see people’s paychecks smaller on Jan. 1 because Congress didn’t act.”

The pact would extend cuts in income tax rates for all earners that would otherwise expire next month, renew long-term jobless benefits and trim Social Security taxes for one year.

Democrats have objected that it is too generous to the rich, especially its provisions cutting estate taxes for the wealthiest Americans. House Democrats voted in a closed-door meeting Thursday not to allow the package to reach the floor for a vote without changes to scale back tax relief for the rich.

Asked about those objections, Obama said there will be talks between House and Senate leaders about the package’s final details.

“Keep in mind, we didn’t actually write a bill,” he said of his agreement with GOP leaders. “We put forward a framework. I’m confident that the framework is going to look like the one that we put forward.”