WASHINGTON -- Barely an hour after President Barack Obama invited congressional Republicans to post-election talks to work together on major issues, the Senate's GOP leader had a blunt message: His party's main goal is denying Obama re-election.

In a sign that combat and the 2012 elections rather than compromise could mark the next two years, Sen. Mitch McConnell on Thursday called for Senate votes to repeal or erode Obama's signature health care law, to cut spending and to shrink government.

"The only way to do all these things it is to put someone in the White House who won't veto any of these things," McConnell said in a speech to the conservative Heritage Foundation.

The Senate Republican leader's confrontational tone was in sharp contrast to the posture Obama took Wednesday in the face of a new GOP-controlled House and Republican gains in the Senate. Obama followed up Thursday morning by inviting Republican and Democratic congressional leaders for talks on Nov. 18 and challenging his own Cabinet to make Washington work better.

"I want us to talk substantively about how we can move the American people's agenda forward," Obama said of the upcoming meeting with lawmakers. "It's not just going to be a photo op."

The meeting in two weeks will be watched for any indication of compromise between Obama and Congress' Republican leaders, House Speaker-in-waiting John Boehner and McConnell. They will be joined by the top Democrats in Congress, House Speaker Nancy Pelosi and Senate Majority Leader Harry Reid.

WATCH: TalkingPointsMemo highlighted the contrasts between Obama's conciliatory speech and McConnell's blatantly partisan aims

Obama said Thursday, "It's clear that the voters sent a message, which is that they want us to focus on the economy and jobs."

Still, there are major differences between the two parties, including the GOP emphasis on tax-cutting, and Obama made that clear on Wednesday.

"From 2001 to 2009, we cut taxes pretty significantly," Obama said, "and we just didn't see the kind of expansion that is going to be necessary" to create jobs.

Obama and, to some degree, Republican leaders did signal they might reach accords on a few issues, such as energy. Obama has abandoned his proposed cap-and-trade system for trying to reduce greenhouse gases, which Republicans sharply opposed. But he said the two parties might reach compromises on other fronts, such as promoting electric cars, nuclear power, energy efficiency and "energy independence."

But McConnell on Thursday indicated that the road to agreements is more like a one-way street.

"If the administration wants cooperation, it will have to begin to move in our direction," McConnell said.

And he spelled out a strategy for undermining Obama's health care law, calling for repeated votes to repeal the measure.

"But we can't expect the president to sign it," he said. "So we'll also have to work, in the House, on denying funds for implementation, and, in the Senate, on votes against its most egregious provisions."

Obama said there should be bipartisan agreement on a plan to give businesses a tax break by letting them accelerate the depreciation of some equipment.

But those are relatively minor issues in the federal universe. The array of Republican and Democratic postelection news conferences Wednesday gave virtually no hint about how Obama and the next Congress might tackle major issues such as immigration or Medicare's long-term viability.

Leaders in both parties talked about cutting spending. But there was barely a word about cutting big programs that consume so much of the federal budget, such as Social Security, Medicare and the military.

Obama hinted that he might be willing to extend Bush-era tax cuts for the wealthiest Americans for a year or two but not make them permanent, as Republicans have advocated.

Republicans, meanwhile, spoke of working with Democrats only in vague terms. Mostly, they seemed defiant.

McConnell was unapologetic for the unified resistance of the Republican Party to Obama initiatives over the past two years.

"By sticking together in principled opposition to policies we viewed as harmful, we made it perfectly clear to the American people where we stood," he said. "And we gave voters a real choice on Election Day."

He also vowed to continue to keep the administration in check by using congressional hearings to oversee executive branch actions.

"Through oversight we'll also keep a spotlight on the various agencies the administration will now use to advance through regulation what it can't through legislation," he said.

Reid, D-Nev., said that in light of the election, "Republicans must take the responsibility to solve the problems of ordinary Americans," although he added, "people expect us to work together."

Big clashes seem inevitable.

On the health care law, Boehner, R-Ohio, told reporters, "We have to do everything we can to try to repeal this bill and replace it with commonsense reforms that'll bring down the cost of health insurance."

Obama, whose veto powers would seem to make repeal impossible, defended the law's main provisions at length.

"When I talk to a woman from New Hampshire who doesn't have to mortgage her house because she got cancer and is seeking treatment, but now is able to get health insurance; when I talk to parents who are relieved that their child with a preexisting condition can now stay on their policy" until age 26, "or the small businesses that are now taking advantage of the tax credits that are provided, then I say to myself, this was the right thing to do," Obama said.

He also rejected claims that he spent too much money to stimulate the economy, bail out banks and shore up automakers at the recession's height. Republicans hammered all those programs in the elections.

"We've stabilized the economy," Obama said. "We've got job growth in the private sectors. But people all across America aren't feeling that progress. They don't see it."

WATCH: TalkingPointsMemo highlighted the contrasts between Obama's conciliatory speech and McConnell's blatantly partisan aims

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In his speech, McConnell said he planned to target Senate Democrats:

"I think the most interesting thing to watch in the next Congress is how many Democrats start voting with us," McConnell said. "Every one of the 23 Democrats up [for re-election] in the next cycle has a clear understanding of what happened Tuesday," he said. "I think we have major opportunities for bipartisan coalitions to support what we want to do."

He also directly challenged Obama:

"As I see it, the White House has a choice: they can change course, or they can double down on a vision of government that the American people have roundly rejected. If they choose the former, they'll find a partner in Republicans. If they don't, we will have more disagreements ahead."