Washington (CNN) -- It's the wildest dream of tea party extremists: the ultimate political comeuppance for the liberal President they love to hate.
Since the day Barack Obama got elected to the White House, they have wanted to force him out.
First, it was the birth certificate. Then, it was the bailouts. A succession of other allegedly impeachable issues followed: IRS targeting, the Benghazi terrorist attack, executive branch overreach.
But it's not going to happen, even if Republicans take back the Senate and retain their House majority in the November congressional elections. Here's why:
No chance: The numbers just don't add up. Under the most optimistic election result for Republicans, they would be far short of the two-thirds Senate majority needed to convict Obama if the House passed articles of impeachment.
Also, a CNN/ORC International Poll last week showed nearly that two in three respondents opposed impeaching the President.
GOP leaders such as House Speaker John Boehner know all that, and so they're trying to tamp down the expectations of their conservative base.
"We have no plans to impeach the President," Boehner said this week. "We have no future plans."
House Budget Committee Chairman Paul Ryan, who may have presidential ambitions in 2016, also quashed the possibility, saying Wednesday that "this does not rise to the high crimes and misdemeanors level" of impeachment.
'Stop just hatin' all the time': Meanwhile, Obama and Democrats talk up the threat to raise money and inspire their supporters to turn out in November.
"Don't boo. Vote," Obama told a Kansas City, Missouri, crowd that voiced its displeasure Wednesday over GOP tactics he criticized.
The President cited the vote by House Republicans authorizing Boehner to sue him over executive actions, saying Congress should instead be passing legislation.
"They're mad because I'm doing my job," Obama said of his Republican foes, urging them to "stop just hatin' all the time."
In debate before Wednesday night's vote, House Democratic leader Nancy Pelosi made sure to link the lawsuit proposal to possible impeachment down the road, calling it a first step to trying to oust the President next year.
The issue resonates with Democratic supporters, according to Rep. Steve Israel of New York, who chairs the Democratic Congressional Campaign Committee. The group has raised $7.6 million online since Boehner announced the lawsuit plan just over five weeks ago, he said.
"You bet we're going to run on a Congress that is just obsessed with lawsuits, suing the President, talking about impeaching him instead of solutions for the middle class, talking about jobs and infrastructure," he said.
'Not how America works': It all makes for grand Washington theater in an election year but reflects deeper political undercurrents, particularly for a right wing already divided between diehard conservatives and more moderate Republicans.
Brown University political scientist Wendy Schiller called impeachment a "farfetched" maneuver that could cause independent voters leaning Republican now to instead vote Democratic in November.
"It reflects in the Republican Party the idea that if you lose an election, you can use every means possible to nullify the result," she said. "That's just not how America works."
Jonathan Chait, a writer who predicted four years ago in a New Republic article that House Republicans would vote to impeach Obama before his presidency ended, said Wednesday that he now doubts that will happen.
Missteps by Republicans, including primary defeats of viable candidates by conservative extremists and the government shutdown they forced last year, "really convinced the establishment that they couldn't indulge the base on all its flights of fancy," Chait said.
GOP pivot: Now Boehner and others want to steer their base away from impeachment, he said, noting that they fear getting pushed into holding a vote that would be politically damaging.
In dismissing an impeachment move, Boehner and Ryan sought to shift the blame for any discussion about it onto Democrats and the White House.
Boehner called it a Democratic fundraising "scam," adding, "They're trying to rally their people to give money and to show up in this year's elections."
Asked about the accusation, White House spokesman Josh Earnest offered a list of Republican legislators who have discussed impeaching Obama in recent months, including Reps. Steve King of Iowa, Ted Yoho of Florida and Steve Stockman and Blake Farenthold of Texas.
The challenge to Boehner and other GOP leaders is to find a middle path between tea party demands to impeach Obama and less extreme options for action, such as the lawsuit.
An impeachment effort after the November election would dominate Washington in the final two years of Obama's presidency, posing possible benefits and risks.
It would divert attention from congressional dysfunction contributing to dismal approval ratings but also could cause the public to blame Republicans for exacerbating that dysfunction.
"We've got a lot of tools at our disposal," Rep. Tom Cole of Oklahoma said, citing such steps as cutting funding for some parts of government disproportionate to the problems.
"Nor do I think you ought to do things in a legislative sense to harass the President," said Cole, who is a Boehner ally. "We've got a disagreement between the two branches, and this is not uncommon. You go to court, and that's what we're seeking to do."
Nixon: The impeachment proceedings against President Richard Nixon and his subsequent resignation still rankle many Republicans today, 40 years later. It was an event that made efforts to remove a sitting president part of routine political discussion in America.
A GOP-led House voted to impeach President Bill Clinton on charges of perjury and obstruction in 1998. The Senate acquitted him on both charges, with none of the minority Democrats voting to convict, and he stayed in office.
Today, any Republican with presidential ambitions -- such as Ryan, perhaps -- wants to avoid making impeachment a reflex response to dissatisfaction with the White House, Schiller noted.
"If you want to be president some day," she said, "the last thing you want is for Congress to be able willy-nilly to impeach you."
CNN's Deirdre Walsh, Kevin Liptak and Paul Steinhauser contributed to this report.