Washington ? President Barack Obama plunged into deadlocked negotiations to cut government deficits and raise the nation’s debt limit Monday, and the White House expressed confidence a “significant” deal with Republicans could be reached. But both sides only seemed to harden their positions as the day wore on, the administration insisting on higher taxes as part of the package but Republican leaders flatly rejecting the idea.

Obama and Vice President Joe Biden met with Senate Majority Leader Harry Reid, D-Nev., for about 30 minutes at the White House, and then met with Senate Republican leader Mitch McConnell of Kentucky for about an hour in the early evening.

White House spokesman Jay Carney said Obama reported after the morning session that “everyone in the room believes that a significant deal remains possible.” But Carney also affirmed that Obama would only go for a deficit-reduction plan that included both spending cuts and increased tax revenue, an approach that Republicans say would never get through Congress.

Obama and the vice president spent more time with McConnell than they did with Reid, an indication of the differences they still need to bridge. McConnell also was seen speaking with White House Chief of Staff Bill Daley moments before his meeting with Obama and Biden.

“The meeting concluded but they will continue to talk,” McConnell spokesman Don Stewart said afterward.

Hours earlier McConnell reaffirmed Republican opposition to more tax hikes in a speech from the Senate floor.

“It’s time Washington take the hit,” he said, “not the taxpayers.”

McConnell said any tax increase or new spending would be counterproductive to economic recovery, and he pointed out that Democrats had been unable to pass tax increases on the wealthy when they controlled both chambers of Congress last year.

“Let’s move past tax hikes, talk about what’s actually possible, and let’s talk about what has and hasn’t worked over the past two years,” said the Kentucky Republican.

Reid said, “I hope my Republican colleagues will put the economy ahead of politics.” Speaking on the Senate floor, he said, “I hope they’ll join us to create jobs and set aside their desire to please the tea party and defeat President Obama.”