House speaker John Boehner has left open the door for a quick bill that would halt tax increases for the vast majority of Americans on January 1.

Boehner twice ducked questions from reporters during a press conference on Capitol Hill on Thursday about whether he was prepared to allow a vote on a bill that would see the top 2% of the country's richest face tax rises but exempt the remaining 98%.

With just over two weeks left until the country goes over the so-called fiscal cliff, the House or Representatives broke up until next week with no deal in place. The Democratic leader in the House, Nancy Pelosi, said if a deal is not reached this week or early next week at the latest, there will be no chance of securing the necessary legislation in time.

One emergency compromise being discussed in Congress is for a short bill to deal with taxes, and leaving spending cuts until next year.

Boehner, the most senior Republican in the House, has consistently expressed opposition to tax rises for the wealthy. Asked at a press conference to give a categorical assurance that he would oppose a bill that would do this, it was significant that he declined. Instead, he said he was not prepared to discuss hypotheticals.

"Ifs and ands and buts are like candy and nuts. If that was the case, then every day would be Christmas," Boehner said. He added: "My goal is to get an agreement with the president of the United States that addresses this problem."

Boehner has been in direct negotiation with Barack Obama in the search for a deal on tax and spending.

With polls showing an overwhelming majority in favour of tax rises on the wealthiest, the Republicans are under pressure, risking taking the blame if every taxpayer sees an increase next month.

The latest poll by Pew, taken between December 5 and 9, found 55% saying that Obama was making a serious effort to work with Republicans on a solution to the deficit problem, and that only 32% felt that way about the Republicans.

Boehner said the main point of contention between him and Obama is the failure of the president to offer specific cuts in spending.

The president had promised a balanced approach, Boehner said. "[But] his proposals have been anything but. He wants far more on tax hikes than on spending cuts, and instead of beginning to solve our debt, he wants new stimulus and to raise the debt limit whenever he wants, without any cuts or reform," the Speaker said. "It is clear the president is just not serious about cutting spending – but spending is the problem."

He added: "If the president will step up and show he is willing to make the spending cuts that are needed, I think we can some good in the days ahead."

The Democratic leader in the Senate, Harry Reid, said the problem was the Republicans, who, in spite of their rhetoric, had failed to agree to tax rises on the wealthiest. "To this day, the Republicans have not identified 5¢ of actual money. They are talking in generalities – 'we'll do revenue, we'll do revenue'. They will not agree to money.

"The only people in America that think the richest of the rich shouldn't pay more money are the Republicans in this building."

Republican senator Jim DeMint, who surprised Washington last week by saying he intended to resign as senator to head up the conservative thinktank the Heritage Foundation, predicted the Republicans will fold on the tax issue.

He told CBS: "The president campaigned on raising taxes and getting rid of the Bush-era tax cuts, and he's going to get his wish. I believe we're going to be raising taxes not just on the top earners; everyone is going to be paying more taxes in the country, and I believe that's what the president wants."