Senate Majority Leader Harry Reid sent a letter to House Speaker John Boehner today offering to go to conference in pursuit of a broader budget deal if House Republicans pass a "clean" six-week funding measure.

"Now we find ourselves at a loggerheads," Reid said in the letter. "There needs to be a path forward to reopen our government and protect our economy. This is a communication to you offering a sensible, reasonable compromise."

Hours before congressional leaders head to the White House last today to meet with President Obama, Reid and Boehner spoke by phone in a conversation Reid described as "cordial."

"My message to him was very simple: We have to stop playing these foolish games that keep coming to us from the other side of the Capitol," Reid said in a news conference.

But Republicans said Reid's offer rests on the presumption that House Republicans will agree to a clean continuing resolution that includes no attempt to defund or delay Obamacare, a measure they've opposed throughout the shutdown fight.

"The entire government is shut down right now because Washington Democrats refuse to even talk about fairness for all Americans under Obamacare," Boehner spokesman Michael Steel said. "Offering to negotiate only after Democrats get everything they want is not much of an offer."

The goal of the budget conference would be to hammer out the differences between the two sides on the 2014 budget, which has yet to be passed.

House Republicans earlier this week proposed a conference on the continuing resolution as a way to end the shutdown, but the Senate voted against it Tuesday.

President Obama is scheduled to meet today at 5:30 p.m. with Boehner, Reid, Senate Minority Leader Mitch McConnell and House Minority Leader Nancy Pelosi to discuss the shutdown and the debt ceiling. Reid did not say what he expects to come from the meeting.

"I didn't call the meeting. The president called the meeting," Reid said. "I think it's important that he listen to what McConnell and Boehner have to say. He knows how Pelosi and I feel."