Thursday's NBC/WSJ News poll finds a major shift among Republicans on whether or not the party should make concessions to Democrats in order to avoid the "fiscal cliff." 

In April, 38 percent of Republicans favored compromise between the two parties on the budget. Now, 59 percent do -- the first majority of Republicans to support compromise in NBC/WSJ polling on the issue.  

Sixty-one percent of Republicans would accept higher taxes on the wealthy as part of a deal. What they are least willing to accept is giving the president the power to raise the debt ceiling without congressional approval. Larger military and defense cuts were also considered unpalatable by most Republicans. 

Even as Republicans express a willingness to compromise, their brand has been badly damaged by the perception that the party is unyielding. Asked an open-ended question as to what single word or short phrase people would use to describe the Republican Party, 65 percent of the responses were negative, while just 17 percent were positive.

Desire for compromise is also at an all-time high among Democrats, at 70 percent. The most acceptable compromise for Democrats would be continuing tax cuts for high-earners; the least acceptable would be larger cuts to Social Security, Medicare and Medicaid.