Here are the key moments from the last day before the financial default deadline, when the Senate and House came together to pass a deal to reopen the government. (The Washington Post)

President Obama and congressional leaders sought Thursday to move beyond the cycle of crisis that has paralyzed Washington for three years, initiating talks over the broad issues at the heart of their fight: the size of government and the level of federal taxation.

Neither Republicans nor Democrats held out much hope that the talks would produce an ambitious deal to spur economic growth or tame the $16.7 trillion national debt. But senior Republicans — whose party suffered in opinion polls after forcing the second-longest government shutdown in U.S. history — said they are unlikely to use that lever to challenge Obama again.

“There’s a country saying in Kentucky: There’s no education in the second kick of the mule,” Senate Minority Leader Mitch McConnell (R-Ky.) said when asked whether another shutdown is possible when the latest government-funding bill runs out in January.

“We’ve seen that movie before,” McConnell said in an interview. “We know how it ends.”

Democrats, meanwhile, noted that Republicans this week agreed to raise the debt limit without extracting concessions — the second time that has happened since the GOP’s reputation was battered by the debt-limit standoff of 2011. At the White House, the Republican surrender raised hopes that Obama’s presidency would no longer be dominated by endless partisan battles over the budget.

“Now that the government is reopened, and this threat to our economy is removed, all of us need to stop focusing on the lobbyists and the bloggers and the talking heads on radio and the professional activists who profit from conflict, and focus on what the majority of Americans sent us here to do, and that’s grow this economy,” Obama said at the White House.

He urged Congress to complete an overhaul of the nation’s immigration laws and a rewrite of federal farm policy, as well as adopt a budget.

“I understand we will not suddenly agree on everything now that the cloud of crisis has passed,” Obama said. But “I will look for willing partners wherever I can to get important work done.”

As Obama spoke, official Washington slowly came back to life after 16 days in shutdown. Federal workers, no longer furloughed, streamed back into the city, emerging from Metro stations to receive cheery greetings from Vice President Biden and Agriculture Secretary Tom Vilsack. At the Capitol, a worker wound the historic Ohio Clock, which had stopped ticking on the shutdown’s eighth day.

Meanwhile, congressional budget leaders met over bagels and cream cheese to begin the difficult work of forging compromise. The agreement struck this week to raise the debt limit until February and fund the government through Jan. 15 calls for a conference committee to resolve differences between separate blueprints for fiscal 2014 adopted by the Republican House and the Democratic Senate.

For much of this year, House Budget Committee Chairman Paul Ryan (R-Wis.) resisted going to conference with Democrats, saying he wanted to wait until he had maximum leverage to seek spending cuts and an overhaul of the tax code. That leverage was Obama’s need for Congress to raise the debt limit.

But the debt-limit fight was hijacked by GOP hard-liners more interested in rolling back Obama’s landmark expansion of health coverage, and Ryan’s moment was lost.

Late Wednesday, he voted against the measure to reopen the government. But at breakfast Thursday, he held out hope that he and Senate Budget Committee Chairman Patty Murray (D-Wash.) could find common ground and report a budget plan by Dec. 13.

“I want to have a budget agreement that gets this debt and deficit under control, that does right by future generations and helps us grow the economy,” Ryan told reporters. “And we’re going to try and figure out if we can find an agreement to do that.”

Democrats, meanwhile, were looking forward to the debate, which will begin in earnest during the last week in October, when the Senate returns from a week-long break.

The Democrats’ budget would restore funding to federal agencies by replacing deep automatic cuts known as the sequester, in part with a large infusion of new tax revenue from the rich. The Ryan budget would not raise taxes and would balance in 10 years, but only by canceling the benefits of the Affordable Care Act while keeping its tax hikes and Medicare cuts.

Ryan would also cut spending by domestic agencies to levels so low that even some House Republicans balked at approving funding bills based on his framework.

“The scope of this conference is everything in the Republican budget and everything in the Democratic budget, and those budgets present a stark contrast in priorities for the country,” said Rep. Chris Van Hollen (D-Md.), the senior Democrat on the House Budget Committee. Van Hollen attended the breakfast with Ryan, Murray and Sen. Jeff Sessions (R-Ala.), his Republican counterpart in the Senate.

Rather than trying to hash out a full budget blueprint, many lawmakers and independent analysts expect the conference committee to focus on the most urgent issue facing Congress: funding federal agencies through fiscal 2014.

Murray’s budget would set agency spending at $1.058 trillion, while Ryan’s budget calls for $967 billion, a level that assumes that the next round of sequester cuts takes effect on Jan. 15.

Both sides are interested in canceling the cuts and replacing them with other savings. Last week, when Republicans were still looking for a deal to open the government and raise the debt limit, House Republicans proposed restoring $100 billion to agency budgets over the next two years.

To avoid increasing deficits, they proposed adopting a range of proposals from Obama’s most recent budget request, such as raising Medicare premiums for high-income seniors and requiring federal workers to contribute more to their retirement.

Democrats have so far insisted on balancing any cuts to Medicare or Social Security with higher taxes on the wealthy. But in an interview with a Cincinnati radio station Wednesday, House Speaker John A. Boehner (R-Ohio) said Republicans would never accept higher taxes.

On Thursday, McConnell found the outlook for compromise equally gloomy.

“There is an openness on our side for trading mandatory spending reductions for sequester spending relief. So far, the Democrats’ view is no mandatory changes without taxes,” McConnell said.

“If you’re trying to look ahead to January and February, the issues will be the same. And the views will be the same,” he said. “And it will be difficult to get an outcome.”

Paul Kane and Rosalind S. Helderman contributed to this report.