Despite a few signs of more open communication between the warring parties in Congress, leaders on both sides insisted publicly that they are sticking to their positions Wednesday as the government shutdown stretched into its second week.

The White House invited all House Republicans to the White House Thursday to discuss the ongoing impasse. But, in response, leaders are sending just an 18-person delegation, aides said. House Speaker John Boehner, Majority Leader Eric Cantor, and 10 additional members of GOP leadership are expected to attend, along with top committee chairmen including Budget Committee head Paul Ryan.

White House spokesman Jay Carney said that the president is "disappointed" that Boehner instructed most GOP House members not to attend the meeting.

"The President thought it was important to talk directly with the members who forced this economic crisis on the country about how the shutdown and a failure to pay the country's bills could devastate the economy," Carney said.

Obama is also expected to meet with Senate Democrats Thursday, a White House aide said.

Democrats from the lower chamber met with the president late Wednesday.

"This is a sad scenario for our country," House Minority Leader Nancy Pelosi told reporters of the ongoing shutdown after Democrats emerged from the meeting.

Pelosi said that she was skeptical of a short-term raise in the debt ceiling, a proposal that some House members are floating as a way to put off a potential U.S. default while lawmakers negotiate a larger solution.

"A short-term debt limit, it doesn't restore confidence," she said. 'When we see [Republicans] offer one, we'll see what path they think that takes us down."

The flurry of scheduling came after Republicans Boehner and Cantor met with top House Democrats Pelosi and Steny Hoyer Wednesday on Capitol Hill.

“Reps. Pelosi and Hoyer asked for the meeting, and as we’ve stated publicly, we're willing to meet with any Democratic leader who is willing to talk,” Boehner spokesman Michael Steel said in a statement.

Shortly after the meeting with Democrats Wednesday, Boehner took to the House floor to again decry the “train wreck” of President Barack Obama’s health care law, even as some members of Boehner’s party suggested that changes to Obamacare should be decoupled from the shutdown fight.

Republican House Speaker John Boehner speaks on the chamber floor Wednesday, reiterating his objection to the Affordable Care Act.

“We need you to sit down and have a conversation about the big challenges that face our country,” Boehner said, addressing Obama.

House Republicans who have been holding firm on attaching Obamacare changes to ending the shutdown are facing some pressure from within.

In a letter, Koch Industries – a conglomerate owned by wealthy patrons of conservative causes -- told members of Congress that it takes “no position” on attaching the health care changes to the shutdown fight. The group instead urgedmembers of Congress to focus on spending reductions.

In an op-ed in the Wall Street Journal Tuesday, top-ranking Republican and Budget Committee head Ryan proposed ending the shutdown and avoiding a default crisis later this month by negotiating “modest reforms to entitlement programs and the tax code.” That proposal did not mention major changes to Obamacare, however, prompting ire from some conservatives who say that the law must be delayed or defunded to protect the American economy.

On the other side of the aisle, Democrats say they’re holding firm to their proposal to negotiate with Republicans only after the debt limit issue has been fixed and the shutdown has been ended.

“Open the government, pay our bills, we’ll negotiate,” Senate Majority Harry Reid said Wednesday.

On Tuesday, Obama suggested that he is open to a short-term raise in the debt ceiling and a reopening of the government in exchange for long-term budget bipartisan negotiations; Boehner called that plan “unconditional surrender.”

House Democrats are slated to meet with Obama Wednesday afternoon.

In another unusual meeting earlier Wednesday, New Jersey Gov. Chris Christie - often referred to as a potential 2016 GOP presidential candidate - met with Senate Minority Leader Mitch McConnell and other Senate Republicans on the Hill.

Christie was in Washington for an event for Sen. Jeff Chiesa, R-N.J., whom Christie appointed as an interim senator when Sen. Frank Lautenberg passed. A Senate GOP aide said that Christie asked to drop by for a "courtesy visit."

Kasie Hunt contributed to this report.

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