President Barack Obama challenged the GOP to end political brinkmanship and said Republicans should "win an election" if they so badly wish to change his policies.

In his first extended remarks since the government reopened, Obama said that the public has grown "fed up" with its government and urged lawmakers to move past the conflict of the past few weeks.

"To all my friends in Congress, understand that how business is done in this town has to change," he said.

"You don't like a particular policy or a particular president? Then argue for your position. Go out there and win an election," The president said. "But don't break it.”

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Whether congressional Republicans could resolve their differences with Obama -- their disagreements have characterized governing in Washington over the past two and a half years -- was very much an open question, though. The public has broadly blamed the GOP for the shutdown, though, and Obama pressed his advantage on Thursday.

"We hear some members who pushed for the shutdown say they were doing it to save the American economy," Obama said. "But nothing has done more to undermine our economy in the past three years than the kind of tactics that create these manufactured crises."

The president further said that "nothing has done more to damage our standing with other countries than the spectacle we've seen the last three weeks," which he said had "encouraged" America's enemies as a byproduct.

Obama didn't single out any Republicans by name, but the implications of his remarks were clear. He alluded to the internal Republican turmoil that has helped fuel the GOP's governing paralysis in recent years. Obama urged Congress to "stop focusing on the lobbyists and the bloggers, the talking heads on radio and the professional activists who profit from conflict" -- a thinly-veiled reference to some of the conservative instigators who helped goad some Republican lawmakers into adopting a hard-lined stance that conditioned government funding on undoing the president's signature accomplishment, the Affordable Care Act.

There are some reasons for optimism. Obama mentioned three priorities: a budget, immigration reform and a farm bill. The House and Senate appointed negotiators to a formal conference committee in the past few weeks to work out differences between their legislation.

And late Wednesday, House and Senate leaders appointed representatives to a similar conference committee to hash out the details of the House and Senate budgets. Democratic and Republican budget leaders had breakfast on Monday, and were conciliatory in their language.

But the next test for Washington will come in January, when the latest tranche of government funding expires.

Immigration also faces a treacherous path forward, as House Republicans have resisted passing the comprehensive Senate bill which gives undocumented residents of the United States a pathway to citizenship.