However, that outcome only came under immense pressure on House Republicans after their partisan proposals seeking to link provisions dismantling or defunding Obamacare were rejected by the Democratic-led Senate and the President.
House Speaker John Boehner's spokesman said the Ohio Republican sought a "step-by-step" process to address the immigration issue, which was Washington code for rejecting Obama's comprehensive approach that would offer immigrants living illegally in the country a pathway to legal status.
Conservatives call that amnesty, and a senior GOP aide told CNN that "the President's attitude and actions over the past few weeks have almost certainly poisoned the well on immigration, at least for now."
Back to work
Before Obama spoke Thursday, federal employees returning to work got muffins from Vice President Joe Biden and hugs from colleagues, along with eye rolls about their "vacation" due to the shutdown.
"I am happy it's ended," Biden said when he arrived at the Environmental Protection Agency with the muffins handed out to returning workers. "It was unnecessary to begin with."
In the basement of the Capitol, there were exuberant hugs as furloughed colleagues were welcomed back, but there was also bitterness toward the elected legislators in charge upstairs.
A common refrain was the sarcastic question: "How was your vacation?" Responses were often nonverbal -- an eye roll, a head shake, an angry glare, the occasional ironic laugh.
Had Congress not approved a debt limit increase, the government would have lost its authority to borrow more money to pay all of its bills. Social Security checks and veterans' benefits could have stopped. The markets could have gone into a tailspin.
Approval of the temporary spending plan meant the return to work of more than 800,000 furloughed employees, while more than 1 million others who've been working without pay will get paychecks again.
A provision in the agreement guaranteed back pay for government workers for the shutdown.
However, the measure doesn't address many of the contentious and complicated issues that continue to divide Democrats and Republicans, such as changes to entitlement programs and tax reform.
"We think that we'll be back here in January debating the same issues," John Chambers, managing director of Standard and Poor's rating service, told CNN on Wednesday night. "This is, I fear, a permanent feature of our budgetary process."
At the White House, Carney hoped the outcome of the shutdown showdown -- with Republicans getting little in return for the public anger leveled mostly at them for causing it -- would revise how things worked.
"It's a new day, and maybe that dynamic will change," he said.
Senate Republican leader Mitch McConnell of Kentucky, credited with brokering the agreement with his Democratic counterpart, Majority Leader Harry Reid of Nevada, said in published interviews Thursday there would be no further government shutdowns.
A $24 billion battle
The partial government shutdown came at a steep cost. Standard and Poor's estimated it took a $24 billion bite out of the economy.
Then there's the impact it had on politicians' image. If there's one thing polls showed that Americans agreed on, it's that they don't trust Congress -- with Republicans bearing more blame than anyone else for what transpired.
While some Republicans, such as tea party favorite Cruz, claimed moral victories in energizing their movement, Boehner didn't even pretend his side came out victorious.
"We fought the good fight; we just didn't win," Boehner told a radio station in his home state of Ohio.
Cruz, despite being in the Senate, is credited with spearheading the House Republican effort to attach amendments that would have dismantled or defunded Obamacare.
Republicans did get a small Obamacare concession: requiring the government to confirm the eligibility of people receiving federal subsidies under the health care program.
However, Republican leaders said dismantling or defunding Obamacare was never going to happen and they criticized Cruz and his tea party cohorts for essentially causing the unpopular shutdown over that effort.