President Obama said Friday that he's confident that Congress would pass the tax deal largely as he had proposed by the end of the year.

The president said that while he expected congressional Democrats to pursue some changes to the tax deal he had negotiated with Republicans, that deal would ultimately "serve as the basis for compromise."

"Here's what I'm confident about: that nobody — Democrat or Republican — wants to see people's paychecks smaller on Jan. 1 because Congress didn't act," Obama said on NPR.

"My understanding is that the Senate's going to vote on the package over the next several days and that at the end of the day, people are going to conclude we don't want 2 million people suddenly without unemployment insurance and not able to pay their rent, not able to pay their mortgage, not able to pay their house note," Obama later added.

The president's compromise comes after a day that saw House Democrats vote to reject the tax deal Obama had proposed earlier this week, which calls for a two-year extension of all expiring income tax rates, a 13-month extension of unemployment benefits, and a compromise on the estate tax and certain tax credits.

The administration has pressed its case for extending those tax cuts in a very public way, pitting them at times against members of their own party, who have vowed not to allow a vote on the tax cuts unless changes are made.

"My sense is, is that there are going to be discussions between both House and Senate leadership about all the final elements of the package," Obama said. "We put forward a framework. I'm confident that the framework is going to look like the one that we put forward."