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The two sides planned to continue discussions Friday, a day after Obama and top administration officials met for 90 minutes with House Speaker John Boehner and other House GOP leaders at theWhite House. No agreement was reported and plenty of hurdles remained, but both sides cast their meeting positively as, for the first time, hopes emerged that a resolution might be attainable, even if only a temporary one.

Obama planned a late-morning White House meeting with GOP senators, who said they would present options of their own for ending the shutdown and debt limit standoff. Determined to resolve the twin crises, the Republicans have reached out to senior Democrats, including New York Sen. Chuck Schumer.

"Let's put this hysterical talk of default behind us and instead start talking about finding solutions to the problems," Senate Minority Leader Mitch McConnell, R-Ky., said at the start of the Senate session Friday, shortly before the White House meeting.

Majority Leader Harry Reid, D-Nev., 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.

A White House statement about Thursday's meeting with House Republicans said "no specific determination was made" but added, "The president looks forward to making continued progress with members on both sides of the aisle."

House Majority Leader Eric Cantor, R-Va., said that the meeting was "clarifying for both sides" and that following a night of negotiations, "hopefully we can see a way forward."

The 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 the 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 Friday.

"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."

Boehner's offer represented give on the part of Republicans, who had been insisting on cuts to Obama's 2010 health care law and other programs as the price for reopening government and extending the debt limit. But they claimed victory on one front, noting that they were in negotiations with a president who had said repeatedly there would be none until the government was open and default prevented.

The speaker's plan — and positive though unenthusiastic words about it from White House spokesman Jay Carney — seemed to spark a good day in the financial world. The Dow Jones industrial average jumped 323 points, or 2.2 percent. European Central Bank head Mario Draghi said that while a U.S. default would inflict "severe damage" on the global economy, the world believes Washington will "find a way out of this."

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.

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.

That has prompted Senate Minority Leader Mitch McConnell, R-Ky., and other GOP senators to seek their own possible resolution to the shutdown and debt limit fights.

"For the first time there seems to be some movement," Sen. John McCain, R-Ariz., said after a meeting with McConnell, R-Ky., and a half dozen Senate Republicans.

Sen. Susan Collins, R-Maine, and others have proposed a six-month extension of government spending, repeal of the medical device tax and greater flexibility for agencies to deal with across-the-board spending cuts in effect this year.

McCain said the goal was ending the shutdown and raising the debt limit, but said, "We will not defund Obamacare," a crucial demand for conservatives.

Reid has proposed extending the debt limit through 2014, which would boost the current $16.7 trillion debt limit by around $1 trillion. He has been planning for a test vote by Saturday on the measure, which has no other conditions, but Republicans may have enough votes to block it unless he agrees to changes.