WASHINGTON – The Obama administration and a group of Republican senators Thursday abandoned efforts to work out a budget deal and avoid a showdown over the national debt, saying they had failed to resolve their long-standing dispute over taxes.

“It’s very evident that there just isn’t common ground at present and we’ve all agreed there’s no reason for these talks to continue,” Sen. Bob Corker, R-Tenn., said after attending the group’s final session at the White House.

Asked what happens next, Corker said, “I have no idea.”

The end of the talks comes just over a week before Congress is to return from its summer break to confront a series of imminent deadlines, including the risk of a government shutdown Oct. 1 and potential default on the national debt a few weeks after that.

President Obama and his team began meeting with eight Republican senators earlier this summer in hopes of reaching an agreement to raise the $16.7 trillion debt limit and replace sharp automatic budget cuts known as the sequester.

The eight were dubbed the Diners Club on Capitol Hill because they had been culled from a larger group of Republican senators who accepted Obama’s invitation in March to dine at the White House and a downtown hotel in hopes of settling a battle over the budget that has dominated Washington since Republicans took control of the House in 2011.

Through multiple meetings with White House Chief of Staff Denis McDonough, Deputy Chief of Staff Rob Nabors and Budget Director Sylvia Mathews Burwell, the group discussed a range of options, including a “grand bargain” that would involve a complete restructuring of Medicare, according to people familiar with the meetings.

The group also discussed a smaller deal that would replace much of the remaining sequester savings — about $500 billion over the next eight years — with narrower reforms to Medicare, Social Security and other mandatory-spending programs, such as farm subsidies.

But the talks never really gelled, in part because Republicans would not consider raising taxes on the wealthy or corporations as part of the smaller deal, arguing that congressional Republicans as a whole would never agree to replace sequester cuts with higher taxes. Nor did they offer a specific strategy for raising taxes as part of the larger deal.

The final meeting came Thursday at the White House, where the group also discussed potential military action against Syria. The eight senators were Corker, Johnny Isakson (Ga.), Daniel Coats (Ind.), Kelly Ayotte (N.H.), John Hoeven (N.D.), Ronald H. Johnson (Wis.), and, joining by phone, John McCain (Ariz.) and Lindsey O. Graham (S.C.). Both sides agreed there was no point in meeting again.

Administration officials said the White House remains open to meeting with the senators and that Obama’s $1.2 trillion plan to replace the sequester — which pairs $600 billion in new taxes with significant cuts to health and retirement programs — remains on the table. Corker suggested Obama will have to open a line of communications with House Republican leaders.