The nation’s brief respite from the serial budget battles that have consumed Washington, D.C., is officially over, with President Barack Obama’s Tuesday demand for new tax revenue in a short-term deal to avoid automatic spending cuts at the beginning of March.

In an appearance in the Brady Press Briefing Room, Obama once again tried to use the bully pulpit to paint the GOP into a corner, using the same fairness playbook that helped him win re-election and a victory on tax rates during the fiscal-cliff deal. This time, the scale may be smaller but the game is the same — in the president’s eyes, either congressional Republicans agree to more new tax revenue or they will bear responsibility for the economic damage and hundreds of thousands of lost jobs from the sequester taking effect.

With the debt ceiling out of the way until May and likely even later, the coming showdown over the sequester is now the main event, albeit one with less of a sense of urgency than a potential default on U.S. government obligations, the fiscal cliff or even an old-fashioned government shutdown.

Both parties seem prepared to test each other’s political pain threshold when it comes to the across-the-board cuts taking effect. There is little evidence of fresh bipartisan talks to avert the cuts, and both parties, once again, are split on the perennially thorny question of taxes. Additionally, some Republicans have hinted they would rather let the cuts go into effect than negotiate any higher taxes with the White House.

After the fiscal-cliff deal netted Obama more than $600 billion in revenue over the next decade from the wealthy, Republicans declared they would not agree to more in future talks. But the White House has made clear it sees the fiscal-cliff deal as only half of a $1.2 trillion tax increase it’d like to see.

On Tuesday, Obama said he wants more revenue even in a short-term package to avert the sequester — which would cut $85 billion in federal spending for the rest of this fiscal year and about $1.2 trillion over the coming decade.

“They should at least pass a smaller package of spending cuts and tax reforms that would delay the economically damaging effects of the sequester for a few more months,” Obama said. He said there was no reason the economy “should be put in jeopardy just because folks in Washington couldn’t come together to eliminate a few special-interest tax loopholes or government programs that we agree need some reform.”

Obama didn’t lay out a specific plan, beyond saying that his grand bargain offer made in December remained on the table, and Press Secretary Jay Carney named assorted tax breaks the president has sought to eliminate, including those on carried interest, corporate jets, oil companies and others.

But Republicans dismissed the idea even before he spoke.

“We believe there is a better way to reduce the deficit, but Americans do not support sacrificing real spending cuts for more tax hikes,” Speaker John A. Boehner, R-Ohio, said. “The president’s sequester should be replaced with spending cuts and reforms that will start us on the path to balancing the budget in 10 years.”

Ways and Means Chairman Dave Camp, R-Mich., dismissed the proposal as “nothing more than another tax hike to pay for more Washington spending.”

While Americans for Tax Reform President Grover Norquist blessed the New Year’s fiscal-cliff deal as a way to prevent a larger, automatic tax hike, any tax increases at this point would certainly be considered a violation of ATR’s no-new-taxes pledge, which most congressional Republicans have signed.

The sequester, included in the August 2011 debt limit deal between the White House and Congress, would cut about $43 billion from Pentagon spending and $26 billion from nondefense discretionary programs in the next seven months of the fiscal year.

Those cuts are now due to hit in March because the fiscal-cliff deal delayed them for two months. But the White House said the uncertainty leading up to the original Jan. 2 deadline already had an effect on the economy toward the end of last year.

The White House last week said uncertainty contributed to a 0.1 percent decline in the gross domestic product in the fourth quarter — an unexpected decline, led in part by falling federal spending.

Obama emphasized at the White House that although the economy is poised to strengthen this year, it should not have to absorb another “self-inflicted wound.”

Boehner earlier Tuesday noted that the House in the previous Congress passed plans to replace the sequester. “It’s time for the Senate Democrats to do their work. It’s time for the president to offer his ideas for how to replace the sequester.”

The Senate did not take up the bills the House passed last year because Democrats said the proposals targeted domestic discretionary spending while sparing defense programs and failing to bring in new revenue.

Senate Majority Leader Harry Reid, D-Nev., has said he hopes to pass a measure to replace the sequester but that it could come after the March 1 deadline passes. It is unclear how federal agencies would respond in their day-to-day operations, but other Democrats said Tuesday that they welcome the new White House approach in the meantime.

“If we can’t agree now on a long-term solution, the best thing for families and the economy would be to pass a balanced short-term sequestration replacement while the House and Senate work on our budget resolutions,” Senate Budget Chairwoman Patty Murray, D-Wash., said.

But while Senate Finance Chairman Max Baucus, D-Mont., signed on to the president’s call for more revenue, he expressed concerns about the effect Obama’s short-term fix might have on a broader tax overhaul effort in Congress.

“When it comes to tax reform, we must avoid the urge for the quick fix,” Baucus said. “We are not going to have multiple bites at this apple. I want to ensure that when we do tax reform, we do it right.”

Daniel Newhauser contributed to this report.