Washington (CNN) - Even as the impasse over the debt ceiling continues, behind-the-scenes talks are underway between Democratic and Republican leaders about a bipartisan deal to end the crisis, according to two Senate leaders intimately involved in the situation.
"There are still discussions going on," said Sen. Jon Kyl of Arizona, the No. 2 Republican in the Senate. "Everybody's talking."
"I continue to believe there are Senate Republicans who are looking for an honest solution," said Sen. Dick Durbin, who is the second-ranking Democrat.
Kyl said he hopes senators reach an agreement before planned votes this week in the House and Senate on separate partisan bills to lift the debt ceiling. Those bills are unlikely to become law but that are sure to increase tensions between the parties, he said.
"The leaders are all committed to a result by the 2nd," Kyl said, referring to August 2, when the debt ceiling will be reached. "So even though they are trying to prepare for the worst, in effect, to have separate more partisan votes, they are cognizant of the need to work together and continue to work together and they're continuing to talk about a lot of different approaches."
Durbin praised Senate Republican Leader Mitch McConnell for having a "responsible" approach to head off the crisis when he introduced a last-ditch proposal to head off default.
"I hope that sentiment is still there and we see it before the end of the week and we can show in the Senate there is a bipartisan way to get through this," Durbin said.
Neither senator – each of whom had just left a party caucus about the crisis – would specify what is under discussion or whether a deal to end the crisis is really possible.
"The question is whether the senators, Democrats and Republicans, can come up with a more reasonable, moderate approach to the problem," Durbin said. "I think he (Sen. McConnell) understands the gravity of this situation in a way that (House Speaker) John Boehner (R-Ohio) does not."