The GOP's biggest image problem? According to a new Gallup poll, Americans think Republicans are "unwilling to compromise."

And this is a bipartisan perception: The complaint is the top concern among Republicans, Democrats, and independents alike. Confusingly, though, while 26 percent of Republicans thought the party was too "inflexible," their second biggest complaint (14 percent) was that GOPers "don't stand up for their positions and "give in too easily."

That split more or less sums up the Republican Party's major predicament. As pressure builds for the GOP to support gay marriage and immigration reform, these numbers are a sign that Republican voters, like their legislators, are divided on whether to embrace change or dig in their heels.

That tension is reflected in broader critiques of the party. Republicans are increasingly divided, while the Democratic Party seems pretty satisfied with where it stands. (Being in power helps.) Democratic voters, while somewhat agreeing with Republicans that their party spends too much money, seem generally happy with President Obama and his fellow Democrats: 51 percent of them say that there isn't anything to dislike about their party. Among Republicans, just 33 percent feel that their party is perfectly likeable.

Does that mean that Republicans will now compromise on issues like immigration, which, considering the GOP's low support among Latino voters, might actually benefit the party? Not likely, says The Washington Post's Aaron Blake:

Despite the poll's finding, individual Republican members of Congress continue to have plenty of incentive to hold firm and resist compromise. A recent Pew Research Center survey found that Republican voters preferred principled stands to compromise by a margin of 55 percent to 36 percent. And the vast majority of Republican members have more to fear in their primaries than they do in the general election. [Washington Post]

In other words, national polls mean less to congressmen campaigning in safely Republican districts than they do to Reince Priebus and the Republican National Committee, whose "autopsy" on the 2012 election suggests that GOP leaders are on the side of compromise.

So what should Republicans do? According to the poll, Americans have generally positive views about the GOP's support for lower taxes and spending, leading Gallup to suggest that the "key to Republicans' regaining favor with Americans is not necessarily to change their positions, but to be perceived as less dogmatic about them and willing to compromise to pass legislation."

As the battle over the sequester demonstrated, compromise by either side — even in the face of grave economic consequences — is never a given.