WASHINGTON » House Republicans are offering to pass legislation to avert a default and end the 11-day partial government shutdown as part of a framework that would include cuts in benefit programs, officials said today.

Republicans also seek changes in the three-year-old health care law known as Obamacare as part of an end to an impasse that has roiled financial markets and idled 350,000 federal workers.

President Barack Obama has insisted he will not negotiate with Republicans over federal spending — or anything else — until the government is reopened and the $16.7 debt limit raised to avert the possibility of default.

Yet, regarding benefit programs, Obama has previously backed an increase in Medicare costs for better-off seniors, among other items, and that idea also has appeal for Republicans.

The White House appeared briefly to wobble on the issue of negotiations on Thursday, until Senate Majority Leader Harry Reid emerged from a meeting with the president to reaffirm it emphatically.

The House Republicans’ plan was outlined Thursday night in a White House meeting that included senior aides to Obama as well as to House Speaker John Boehner and Majority Leader Eric Cantor, several hours after Obama met with top Republicans.

Without confirming any of the details under discussion, Cantor said, "We’re waiting to hear" from administration officials.

In addition to ending the shutdown and increasing the debt limit, under the proposal Congress and the White House would explore ways to ease across-the-board federal budget cuts that began taking effect a year ago, and replace at least part of them with benefit-program curbs that have been included in recent presidential budgets. Officials who described the approach did so on condition of anonymity, saying they were not authorized to discuss private conversations.

With the weekend approaching, and the deadline for raising the debt limit five days away, Senate Republican Leader Mitch McConnell said it was time to "put this hysterical talk of default behind us and instead start talking about finding solutions to the problems."

A short while later, McConnell led Senate Republicans into a meeting with Obama at the White House, a session that lasted about 90 minutes.

Additionally, the House voted 248-176 to provide funds for nuclear arms research and security despite the shutdown. It was the latest GOP bill aimed at reviving popular programs during the shutdown — and the latest to die in the Senate, where Reid has rejected bills that fall short of fully reopening the government.

While much of the attention has been focused on the House in recent days, McConnell and other Republicans have been exploring possible legislation to avert the default and end the shutdown and to require the White House to make relatively modest concessions on the health care law. Among the possibilities is a repeal of a medical device tax in the law, or perhaps stronger income verification requirements for individuals who receive federal subsidies to purchase coverage.

Determined to resolve the twin crises, the Republicans have reached out to senior Democrats, including New York Sen. Chuck Schumer.

Senate Majority Leader Reid rejected the notion of a six-week increase in the nation’s borrowing authority, pressing not only for a longer, 15-month measure but a reopening of the government.

Thursday’s talks were held shortly before a Wall Street Journal/NBC News poll was released bearing ominous news for the GOP. It showed more people blaming Republicans than Obama for the shutdown, 53 percent to 31 percent. Just 24 percent viewed the GOP positively, compared with 39 percent with positive views of the Democratic Party.

Boehner, R-Ohio, brought a proposal to Thursday’s White House meeting to extend federal borrowing authority through Nov. 22, conditioned on Obama’s agreeing to negotiate over spending cuts and the government shutdown. But participants said the discussion expanded to ways to quickly end the shutdown, which entered its 11th day today.

"It’s clear he’d like to have the shutdown stopped," House Appropriations Committee Chairman Hal Rogers, R-Ky., said of Obama. "And we’re trying to find out what he would insist upon" to reopen the government "and what we would insist upon."

One major problem for Boehner’s plan was highlighted by Senate Majority Leader Harry Reid, D-Nev. After he and fellow Senate Democrats had their own White House meeting with Obama, Reid said negotiations before the government reopens — a key part of Boehner’s proposal — were "not going to happen."

The shutdown has idled 350,000 civil servants, prevented the Social Security Administration from revealing next year’s cost-of-living increase for recipients and curtailed many consumer safety inspections. Officials warn of deeper cutbacks in services if it goes on.

The Obama administration has warned that the government will exhaust its borrowing authority on Oct. 17 and risk being unable to pay its bills and facing default.

"It would be a grave mistake" to ignore the risks to the U.S. and world economy that a default would raise, Treasury Secretary Jacob Lew warned the Senate Finance Committee on Thursday.

House Republicans’ insistence on spending cuts and deficit reduction come with the 2013 budget shortfall expected to drop below $700 billion after four years exceeding $1 trillion annually.

But their insistence on cuts in the health care law as the price for reopening government has frustrated many Senate Republicans, who see that battle as unwinnable.

Associated Press writers Julie Pace, Jim Kuhnhenn, Andrew Taylor and Donna Cassata contributed to this report.