WASHINGTON - As talks shifted from the House to the Senate today, Senate Majority Leader Harry Reid and Minority Leader Mitch McConnell took the lead on striking a deal to end the government shutdown and raise the debt ceiling - the first time the two are talking about the budget impasse.

"The conversations were extremely cordial but very preliminary of course," Reid said at a news conference today. "I hope that our talking is some solace to the American people and to the world. This hasn't happened until now.

"This should be seen as something very positive," he added.

McConnell requested a meeting with Reid last night to jump start talks on the fiscal standoff. The two met in Reid's office at 9 a.m. Saturday for an hour-long meeting that included Sen. Lamar Alexander, R-Tenn., and Sen. Chuck Schumer, D-N.Y.

"The meeting that Senator Reid and I had with Senator Alexander and Senator McConnell gives me a little bit of cause for optimism," Schumer said. "Clearly the talks are in their very early stages, but I believe Senator McConnell showed good will. I believe he wants to come to a solution."

The contours of a potential deal have yet to emerge, but Reid said he is open to negotiating on the lengths of the continuing resolution and the debt limit increase.

"We are negotiating that. I'm not locked in stone," Reid said.

(Credit: Drew Angerer/Getty Images)

Conversations to craft a deal moved to the Senate this weekend after President Obama rejected the proposal from House Republicans that called for a six-week debt limit suspension in exchange for an agreement to negotiate deficit reduction and government funding with Congressional Democrats.

"It will be the Senate that will have to come to an agreement here because the House Republicans seem so divided and in such disarray. They don't have a plan," Schumer said.

Sen. Susan Collins, R-Maine, was working on a bipartisan plan that would reopen the government for six months and raise the debt ceiling until the end of January as well as delay the medical device tax for two years. But Reid officially rejected the proposal, saying the plan "is not going any place at this stage."

Democrats noted that many Republicans are now moving away from making Obamacare an issue in the budget fight.

"Obamacare is no longer their number one issue. Their number one issue is to do anything they can to divert attention from the fools they've made of themselves on Obamacare," Reid said.

Senate Democratic leadership met with Obama at the White House this afternoon.

ABC News' John Parkinson contributed to this report.