John Boehner

Speaker of the House John Boehner, R-Ohio, and GOP leaders talk to reporters following a Republican strategy session at the Capitol, in Washington, Tuesday, Sept. 10, 2013. Boehner, who has supported President Obama's call to use force against Syria as punishment for allegedly using chemical weapons, said he is skeptical of Syria's offer to turn over chemical weapons to international monitors. Boehner added that but President Obama has not yet sold the American people on the need for military action. (AP Photo/J. Scott Applewhite)

House Republicans met privately Tuesday morning to discuss strategy in the eighth day of the government shutdown.

According to Politico, Republicans talked about ways to get Democrats to compromise on both a budget bill and the debt ceiling, including tying them to back pay for government employees who have been furloughed.

House Speaker John Boehner, House Majority Leader Eric Cantor and House Majority Whip Kevin McCarthy brainstormed with other member of the GOP in the meeting that started at 8 a.m.

“A position of not negotiating is not a sustainable option,” Cantor said during a news conference following the meeting.

Boehner told reporters he would like to open the door to a conversation between both sides.

"I'm not drawing any lines in the sand," he told reporters. "It's time for us to sit down and resolve our differences."

Some congressional Republicans see tying employees' back pay to budget issues as a gimmick. Others are considering a short-term deal that would include a debt ceiling increase coupled with spending cuts.

In the Senate, separate party caucuses are expected to meet to tackle raising the debt ceiling before the Oct. 17 deadline.