In an interview with VOA's Press Conference USA, Ornstein predicted the Democratic president would face a series of such face-offs with Republican lawmakers over government spending and taxes during his second and final term.
The first stage of mandated spending cuts, known as sequestration, took effect on March 1. About $85 billion is being cut from the budgets of government agencies as part of a plan that could lead to $1.2 trillion in cuts over 10 years.
Meanwhile, congressional Republicans and Democrats have been debating provisions to fund the government for the rest of the fiscal year and avoid a possible government shutdown later this month if no deal is reached.
Ornstein said that while Americans generally oppose the sequester and a government shutdown, the "broader public opinion" and "political dynamic" on the issues may be of less significance to Republicans.
"In their districts, what they are hearing is 'bring this president down,' 'take him on,' and 'cut the budget,' " Ornstein of the Republicans in Congress.
He said Republicans are also trying to avoid upsetting their local support base ahead of next year's congressional elections and the 2016 presidential race. Republicans have a majority in the House of Representatives and are hoping to capture a majority in the Senate.
REPUBLICAN POLITICAL FUTURE
Ornstein said next year's congressional elections are coming at a time when the Republican Party is deeply divided. He said the dominant factions within the party are conservative.
"Missing from the debate and the dialogue, by and large, is what used to be a very significant force in the Republican Party -- moderate Republicans, centrist Republicans," said Ornstein.
"There are none of them in the House of Representatives anymore," he said, and "one or two" in the Senate. "By and large, they are not a force at all."
OBAMA'S SHIFTING STANCE
Meanwhile, Ornstein said he has seen a shift in President Obama's negotiating strategy with Republicans since he first took office in 2009.
He said Obama's first term strategy centered on "transcending" partisanship by offering compromises. "The other side saw it as a sign of weakness," said Ornstein.
He said Obama is now emulating the negotiating style of former President Ronald Reagan, who was a Republican.
"What Reagan did so well and so famously was he would take a position and say over and over again, 'This is it. I am not moving. This is where I am going to be,' " said Ornstein.
He said after Reagan's opponents offered a series of concessions, the president would say, "Now let's negotiate." As a result, Ornstein said Reagan would end up getting "three-fourths" of what he originally wanted.
Ornstein said Republicans are not happy that President Obama has adopted this strategy. They are complaining, he said, that Obama is taking on a "weakened Republican Party and making it much harder for them."
LOOKING TO THE FUTURE
Ornstein also said one reason why the Democratic and Republican parties are finding it difficult to compromise is because they have set up "exaggerated images" of each other.
He said the parties are "demonizing" each other's positions on issues, which makes it much harder to reach compromises on issues such as the federal budget or economic policy.
On a more optimistic note, Ornstein said if lawmakers can get past their initial confrontations on fiscal issues, the nation would not be that far from stabilizing its debt.
He said 2013 could turn out to be a "remarkably productive year," which would be unusual for a second term president.