Obama Thursday praised "Democrats and responsible Republicans ... for getting together and getting this job done."
He also laid out three areas he believed could be approved in a bipartisan manner by the end of the year: a "balanced approach" to a long-term budget, immigration reform and a farm bill.
Concerning the "politics of this shutdown, let's be clear: There are no winners here," Obama said.
"These last few weeks have inflicted completely unnecessary damage on our economy," the president said. "We don't know yet the full scope of the damage, but every analyst out there believes it slowed our growth."
The government's reopening and extension of the borrowing authority came after the Senate and the House voted to reopen the government through Jan. 15, suspend the debt ceiling through Feb. 7 and lay the groundwork for talks over broader budget issues.
Obama signed the bill into law about 12:30 a.m. Thursday. The Senate vote Wednesday night was 81-18, with 27 Republicans joining 54 Democrats in voting yes. A few minutes later, the House approved the measure 285-144, with 87 Republicans voting in support of the measure. All 198 Democrats who voted supported the measure.
The president said lawmakers should never threaten the nation's financial stability again, quoting from a credit rating agency that said "repeated brinksmanship" was the only thing putting the country at risk.
He also said there was "no economic rationale" behind the actions of some within the conservative wing of the Republican Party to force a partial government shutdown on Oct. 1 and take the country to the brink of default.
"Nothing has done more to undermine our economy in the past three years than the kind of tactics that create these manufactured crises," Obama said, noting the American public was "are completely fed up with Washington."
"But all my friends in Congress understand that how business is done in this town has to change because we've all got a lot of work to do on behalf of the American people," Obama said, "and that includes the hard work of regaining their trust."
"Our system of self-government doesn't function without it," he said.
Now that the government has reopened, "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, create good jobs, strengthen the middle class, educate our kids, lay the foundation for broad-based prosperity and get our fiscal house in order for the long haul," Obama said. "That's why we're here. That should be our focus."
He said he recognized that there would be disagreements, but the two parties must push through their disagreements, focus on areas of agreement and "get some stuff done."
He noted that the bill he signed requires the House and Senate to work on a long-term budget.
"[We] shouldn't approach this process of creating a budget as an ideological exercise -- just cutting for the sake of cutting. The issue's not growth versus fiscal responsibility. We need both," Obama said. "We need a budget that deals with the issues that most Americans are focused on: creating more good jobs that pay better wages."
Concerning immigration reform, Obama noted the Senate passed a sweeping bill earlier this year and it was awaiting action in the House.
"[Economists] estimate that, if that bill becomes law, our economy would be 5 percent larger two decades from now, that's $1.4 trillion in new economic growth," Obama said.
Finally, Obama called on Congress to "pass a farm bill, one that American farmers and ranchers can depend on; one that protects vulnerable children and adults in times of need; one that gives rural communities opportunities to grow and the long-term certainty that they deserve."
Obama called on both parties together to make government work "instead of treating it like an enemy -- or purposely making it work worse."
Without naming names or singling out either chamber, Obama said, "[If you] don't like a particular policy or a particular president, then argue for your position, go out there and win an election. Push to change it, but don't break it. Don't break what our predecessors spent over two centuries building. That's not being faithful to what this country's about."
He closed his remarks by thanking the federal employees who either worked without pay or where laid off during the shutdown.
"What you do is important and don't let anybody else tell you different," he said."
"And those of us who have the privilege to serve this country have an obligation to do our job as best we can," Obama said. "And we come from different parties, but we are Americans first. And that's why disagreement cannot mean dysfunction. It can't degenerate into hatred."