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The announcement by President Obama, Senate Majority Leader Harry M. Reid (D-Nev.) and Senate Minority Leader Mitch McConnell (R-Ky.) Sunday night that a debt-ceiling deal had been reached after months of negotiations marked a significant breakthrough in a process that more than once had appeared to have broken down.

Although the agreement faces tough odds for passage before Tuesday’s deadline, its emergence brings with it revelations about the significance of the months-long debt-ceiling fight for both political parties as well as the White House.

If the debt negotiations were a political campaign, up until Sunday afternoon, the debate about raising the country’s $14.3 trillion borrowing limit would have been in the primary-election phase of the process.

Party leaders in each chamber had announced their debt plans last Monday and lobbied rank-and-file members for support.

In the case of House Speaker John A. Boehner (R-Ohio), that process proved particularly contentious, as House Republican leaders had to rework their plan — twice — to secure the backing of conservative members.

In Reid’s case, the task was somewhat easier — his plan garnered the support of all but three Senate Democrats on Sunday, although it fell short of the 60-vote threshold necessary for passage in the chamber.

After the upper chamber voted to table Reid’s proposal, the debt talks shifted into general-election mode.

And it was then that the stakes for both parties began to come into focus.

Since early May, congressional leaders and the White House have held hours upon hours of meetings during which they’ve worked out the details of a long-term deficit-reduction plan. They’ve tangled over discretionary spending, mandatory spending, comprehensive tax reform, corporate tax loopholes, trigger mechanisms, entitlement reform and the chained consumer price index.

Now, with a deal that could extend the debt ceiling through the end of next year and achieve $3 trillion in deficit savings, members on both sides of the aisle are arguing that the devil is in the details.

In fact, the opposite is true.

When the dust settles on Wednesday, if Congress passes an agreement to raise the limit in exchange for a package of far-reaching spending cuts and fundamental changes to the way Washington spends taxpayer money, it will represent the most significant political development since the 2010 midterm election — and a pivotal moment in the Obama presidency.

As far as details go, the potential deal McConnell outlined Sunday morning hews more closely to Reid’s debt-limit proposal than to Boehner’s.

The plan would extend the debt ceiling through the 2012 election instead of through the next six months — providing Democrats with the certainty of not having to engage in a second debt-limit fight during a presidential election year.

It would not call for Congress to send a balanced-budget amendment to the states to raise the debt ceiling — handing a defeat to conservatives who have rallied behind a plan to “cut, cap and balance” the federal budget.

And although it would not include the deficit savings from winding down the wars in Iraq and Afghanistan (as included in Reid’s plan), the deal would make good on Reid’s proposal for a committee to come up with a broader deficit-reduction framework or else a “trigger” would come into play, forcing additional cuts and, potentially, tax increases.

But as far as the bigger picture goes, the advantage goes to the Republicans, who will have for the first time transformed a routine vote to raise the federal borrowing limit into an opportunity to deliver on their pledge to reduce the size of government.

Ever since they assumed the majority in the 112th Congress, House Republicans have outlined a plan to take “three bites at the apple” when it comes to federal spending. They were successful with their first bite (the April deal on averting a government shutdown) and took some political heat from Democrats with the second (the House vote on the 2012 budget).

The third bite — the debt-ceiling battle — appears to have been the most successful by far.

“To me, the powerful win that Republicans will achieve here is to have changed the debate,” Sen. Mike Crapo (R-Idaho), a member of the bipartisan Gang of Six, said Sunday afternoon as congressional negotiators neared agreement.

“I guess I would put it this way,” he said. “The entire focus in Congress has changed from a complete willingness to overlook the debt and just ‘spend our way into prosperity.’ It has changed to now focusing on how do we control our debt and restrain . . . the negative impacts that our mounting debt has on our economy.”

Democrats would argue that one of the greatest factors contributing to that mounting debt has been the extension of the George W. Bush-era tax cuts. And that’s a battle that both parties are likely to continue fighting both on and off Capitol Hill through November 2012.

But contrast Republicans’ view of their big “win” on the debt ceiling to the Democrats’ response when asked the same question.

Asked what the best thing about the deal was for Democrats, Senate Budget Committee Chairman Kent Conrad (N.D.) — also a member of the Gang of Six — said Sunday afternoon that it was “absolutely the assurance that there’s going to be an extension of the debt limit to avoid a default.”

But wasn’t that just the status quo? Wouldn’t Congress usually raise the country’s debt limit as a routine matter?

“That was the status quo? Absolutely,” Conrad responded. “You used the word ‘usually.’ As you know, this has been a most unusual situation.”

He continued: “You know what, I’m much more interested in what’s the effect on the country than either party. And for the country, we are dealing with an extension of the debt limit. A failure to do so would’ve been catastrophic. I’m much less interested in sorting out pluses and minuses on this side and that side. This is a negotiation; both sides are not walking away with everything they’d like, that is for sure.”

Reid’s floor remarks as he announced the agreement Sunday night reflected that despite controlling two-thirds of a divided government, Democrats were on the defensive when it came to the debt battle.

“The compromise we have agreed to is remarkable not only because of what it does, but because of what it prevents: a first-ever default on the full faith and credit of the United States,” he said.

What the deal means for the White House is not the same as what it means for Democrats on the Hill.

The debt-limit talks were not a political campaign, but Obama faces a tough election in 2012 — and by claiming ownership of the debt agreement, the White House may guard itself against charges from GOP presidential hopefuls that it has not taken serious steps to put the country’s fiscal house in order.

The big risk is a disaffected Democratic base — but as both the debt-limit talks and last year’s tax-package agreement have demonstrated, that’s a gamble the White House appears willing to take.

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