All eyes turned Thursday to the Senate, as leaders there gaveled the chamber back into session and House Republicans ramped up pressure for a fiscal cliff deal to emerge from the Senate after failing to move their own proposal last week.

According to a White House official, President Barack Obama spoke with top congressional leaders in separate phone calls late Wednesday before he left Hawaii to return to Washington: Senate Majority Leader Harry Reid, D-Nev., Speaker John A. Boehner, R-Ohio, Senate Minority Leader Mitch McConnell, R-Ky., and House Minority Leader Nancy Pelosi, D-Calif. They discussed the fiscal cliff, but the official did not provide more detail than that.

Almost every major budget or tax deal this Congress has originated from Capitol Hill negotiators, whether it was to stave off government shutdowns or default or to extend the payroll tax holiday. But with only four days left before their Jan. 1 deadline — when all tax rates are set to rise and across-the-board discretionary spending cuts are set to kick in — leaders have very little time to haggle out an agreement.

Moreover, it appears House GOP leaders either don’t want to be at the table or perceive that they can’t be. The chamber is only in pro forma session, and Senate Democrats haven’t displayed much interest in moving from their current position, which is that the House should pass a Senate-approved extension of tax breaks for income under $250,000.

As the Senate reconvened Thursday morning, Reid came out swinging. He needled Boehner for failing to secure the votes for a backup tax cut plan last week and doubled down on his position that the House pass the Senate’s bill.

“I don’t know, time-wise, how [a deal] can happen now. Everyone knows we can’t bring up anything here unless we do it by unanimous consent,” Reid said, after attacking House Republicans for not reconvening in Washington. “I can’t imagine their consciences. They’re out wherever they are around the country, and we’re here … they couldn’t even get the leadership together yesterday. They had to do it with a teleconference.

“If we go over the cliff, we’ll be left with the knowledge that it could have been prevented with a single vote in the Republican-controlled House,” Reid continued, referring to the tax bill approved by the Senate. That bill, however, would need help via consent from Senate Republicans, as well, given that it cannot become law as a result of a blue-slip issue, meaning that because the legislation generates revenue it must originate in the House.

McConnell was not present on the floor during or immediately after Reid’s remarks.

Reid’s floor remarks were the first public statements made by a key figure in the talks since Obama delivered a brief address Dec. 21 at the White House before departing for Hawaii. Obama also met with Reid that day, when they discussed his most recent offer to Republicans: an extension of current tax rates for income below $250,000, an extension of unemployment insurance benefits and a delay in the sequester, or scheduled spending cuts.

On Wednesday, Treasury Secretary Timothy F. Geithner sent letters to congressional leaders informing them the government would hit its debt limit Dec. 31 and that he would begin to take “extraordinary measures” to continue to pay debts and obligations the government already owes.

When Obama made his public comments Dec. 21, he did not speak about whether an agreement would include an increase in the country’s borrowing capacity and did not mention the terms “debt limit” or “debt ceiling” in his remarks.

During the last lame-duck session, the White House and congressional Democrats did not take the GOP’s threats on the debt limit seriously, a political miscalculation that in many ways helped create the fiscal cliff by necessitating a budget agreement in 2011 that included both immediate and delayed cuts in the form of the sequester, one of the other key pieces of the cliff.

At the end of November, Geithner, on behalf of the White House, asked congressional leaders for a change in how the debt limit is extended, putting the onus on Congress to disapprove of an extension. Republican leaders scoffed.

Boehner has vowed to seek cuts commensurate to the amount the debt limit is increased and the House GOP has clung to the idea that it can use the debt ceiling in early 2013 to wrangle more spending concessions from Democrats.

The details of the most recent offerings from Obama, at least the details that have been made public, have not included proposals on how to deal with the looming need to raise the debt ceiling. Democrats currently hold a position of leverage in the overall talks, especially after Boehner failed last week to move a standalone tax bill that would have raised rates on millionaires, and they might not be willing to concede it at this point for a deal that leaves them in a bind by February or March, when the Treasury runs out of options on fudging with the debt limit.

Senate aides say they’ve been pushing for a debt limit increase for weeks now, but most of the public debate and focus has been on the expiring tax breaks and the bill they currently are pushing House Republicans to take up only deals with taxes.

On the issue of the looming tax increases, House Republicans and Senate Democrats exchanged statements Wednesday in the sort of he-said-she-said that has become the trademark of the latest iteration of congressional budget debates. First, House Republican leaders issued a joint statement targeted at Senate Democrats, followed shortly by a statement from a Reid spokesman.

“The House has acted on two bills which collectively would avert the entire fiscal cliff if enacted. Those bills await action by the Senate,” House GOP leaders said in their statement. “If the Senate will not approve and send them to the president to be signed into law in their current form, they must be amended and returned to the House. Once this has occurred, the House will then consider whether to accept the bills as amended or to send them back to the Senate with additional amendments. The House will take this action on whatever the Senate can pass, but the Senate first must act. The lines of communication remain open, and we will continue to work with our colleagues to avert the largest tax hike in American history.”

“The Senate has already rejected House Republicans’ tea party bills, and no further legislation can move through the Senate until Republicans drop their knee-jerk obstruction,” the Reid spokesman shot back shortly thereafter. “Right now, the Senate bill is the only bill that can become law, and House Republicans owe it to middle-class families to let it pass with Democratic and Republican votes.”

The intransigence of both sides has made a deal against the clock seem increasingly unlikely. But if anything gets brokered, it likely now has to come from the Senate, where Reid and McConnell largely negotiated the August 2011 debt deal that helped bring Congress into the situation it finds itself now. Senate Republican aides suggested McConnell might get involved in talks but that Senate Democrats have to bring something else to the table than the tax bill they’re pushing. McConnell could serve as a key figure in any solution, sources say, but whether his involvement is imminent or would only increase in a post-cliff scenario was not immediately clear.