WASHINGTON — As President Barack Obama waits for the House of Representatives to approve a “fiscal cliff” deal the White House played a central role in negotiating, his aides said they believe the deal struck late Monday has produced a victory for the president and a “sea change” in Republican opposition to tax increases.

Obama had at first sought a big fiscal deal that would have wiped the legislative slate clean for other priorities. That proved impossible, and Obama and his aides are now laying the groundwork a long slog of fiscal fights. In the coming weeks, Obama will deliver an inaugural address and a State of the Union speech with the nation caught up against the debt ceiling, the need to pass a temporary budget measure, and another fight over mandatory spending cuts, and Republicans are dead set on exacting spending cuts to deal with each of them.

Speaking Monday afternoon in the Eisenhower Executive Office Building even before the final deal had been struck, Obama celebrated having pushed Republicans to let taxes go up on the wealthiest Americans — a sticking point in nearly two years of on-and-off negotiations — and anticipated objections from his liberal allies, who argued that he was the one who had capitulated by not raising taxes on all income above $250,000.

“Keep in mind that just last month Republicans in Congress said they would never agree to raise tax rates on the wealthiest Americans,” Obama said before an audience described by the White House as “middle class Americans.” “Obviously, the agreement that's currently being discussed would raise those rates and raise them permanently.”

In this view, the talks were a victory for the president in which Republicans signed off on a deal raising $620 billion in revenue — the first major tax increase in two decades — but only cutting about $15 billion in spending. In the terms of the running negotiations, of the $1.2 trillion in revenue Obama called for in the failed grand bargain, at least $500 billion remains on the table for Obama to push for in subsequent deficit talks.

White House officials believe Republicans have crossed the Rubicon on taxes, agreeing to — and indeed, proposed — significant revenue increases for the first time in two decades.

“It’s a sea change,” one senior official told BuzzFeed Monday before the final agreement was struck. “It will inevitably make it easier to get [Republicans] on board whenever we ask for new revenues, because they’ve already crossed that threshold.”

“That’s the legacy of this debate,” the official said of the bitter negotiations, which wrecked holiday plans across the capital and ended Obama’s first term on a bitter note.

The situation may not be that simple. The Republican vote on higher taxes came after a set of tax cuts had expired and all the votes Monday were, technically, to cut taxes.

And Republicans believe the deal serves as a “reset” point in the president’s relations with Congress, after Obama held all the cards with taxes rising on all Americans at the start of the New Year. With the high-profile tax cuts dealt with, the party can now return to battering the president over $1 trillion in annual deficit spending.

“The president was so adamant about a comprehensive deal because he knows he has less leverage after the middle class tax cuts are released from their “hostage” taker,” said one GOP leadership aide. “With the rich presumably now permanently “paying their fair share,” he’s going to have a lot harder time avoiding spending cuts in a fight over the debt limit, continuing resolution, sequester, etc.”

On Monday Obama expressed openness to further spending cuts — particularly dealing with the growing cost of Medicare — but demanded that they, like any effort to avert the mandatory defense spending cuts in the fiscal cliff, incorporate new revenues from the wealthy.

“The same is true for any future deficit agreement,” Obama said. Obviously, we’re going to have to do more to reduce our debt and our deficit. I’m willing to do more, but it’s going to have to be balanced. And on tax reform, Obama signaled that he would not support revenue-neutral efforts to broaden the base and lower the rates, as Republicans demand.

“There is absolutely no appetite among Republicans to incorporate revenues in raising the debt ceiling,” said a Senate GOP aide, strongly doubting the party’s appetite for any more revenue.

But with Republicans gearing up for a fight over the debt ceiling, and Obama repeatedly saying he will not negotiate over Congress’ responsibility to raise the nation’s borrowing limit, the deal struck by Vice President Joe Biden and Senate Minority Leader Mitch McConnell gives Obama an out.

The two-month delay to the mandatory budget cuts aligns almost perfectly with the expiration of the Treasury Department’s extraordinary measures to prevent the U.S. government from defaulting on its debt, as well as the expiration of the current temporary resolution funding the federal government. Obama could avoid negotiating on the debt ceiling by negotiating to avoid the rest of the sequester — a package of automatic cuts to defense and other spending — and including the borrowing limit in the final agreement. But Obama appears likely to demand a deal similar to the one he achieved Monday — in which the cuts are averted by a 50-50 split of targeted spending cuts and revenue increases, with a 50-50 split on the spending cuts between defense and non-defense appropriations.

“We think that establishes a good precedent,” said another senior White House official.