President Barack Obama and Speaker John A. Boehner traded offers again this week aimed at averting the fiscal cliff, according to GOP staff, but key House Republicans continue to express little confidence that negotiations are moving along.

“We sent the White House a counteroffer that would achieve tax and entitlement reform to solve our looming debt crisis and create more American jobs,” Michael Steel, spokesman for Speaker John A. Boehner, R-Ohio, said Tuesday. “As the speaker said today, we’re still waiting for the White House to identify what spending cuts the president is willing to make as part of the ‘balanced approach’ he promised the American people. The longer the White House slow-walks this process, the closer our economy gets to the fiscal cliff.”

The House GOP offer came in response to a previously unreported second offer from Obama. In that offer, the president dropped his demand for new revenues from $1.6 trillion to $1.4 trillion.

An administration official confirmed that the White House presented House Republicans with a new proposal Monday, adding that the president and speaker spoke by phone Tuesday evening after the White House received the GOP’s response.

The speaker’s office declined to release any specifics of the proposals, but GOP leaders exiting a meeting in Boehner’s office Tuesday afternoon were skeptical that the talks are moving forward with any progress.

“I think the president keeps changing what he’s asking for, so [I feel] less confident,” Majority Whip Kevin McCarthy, R-Calif., told reporters, when asked whether he is more or less confident.

Similarly, Rep. James Lankford, R-Okla., who will take the helm of the Republican Policy Committee next year, said talks are still at a stalemate and that his sense is that the issue will not be solved by the end of the week.

“No, not by the end of the week. I didn’t get any sense of that at all. The president is still focused on raising taxes and not on cutting spending at all. The challenge is the president wants the Clinton tax rates, but he doesn’t want the Clinton level of spending,” he said. “We’re still at a stalemate to try to figure out when the president is going to focus in on spending.”

Still, he said the lines of communication remain open.