According to a recent Pulse Opinion Research poll, 55% of likely voters support a plan that "does not raise taxes, cuts $5 trillion and balances budget. Only 28% support a plan that has "$1 Trillion in Tax Hikes & 100 Billion in cuts that does not balance budget". The first of those is the Paul Ryan House GOP budget. The second is the Patty Murray Senate Democrat budget.
The second question is about how to reduce the deficit generally. An even larger majority, 65%, said it should be done mostly by cutting spending (the GOP plan), while only 24% said it should be done mostly by raising taxes (the Democrat plan).
It would make sense then if a majority of people said they approved of the GOP on budget issues, right? Wrong. In the same poll, only 30% support Republicans more on the budget. The plurality, 35%, actually support Democrats. Actually 4% more people support neither party more than Republicans (technically, this is the correct position based on history).
That leaves only reason #2. The GOP brand is so damaged that even when people agree with them they refuse to admit it. There's more evidence for this phenomenon too.
One of the major problems with thinking on the right during the last election cycle was our assumption that the polls were wrong, that they were oversampling Democrats and undersampling Republicans, thus being skewed to show Obama winning when he wasn't. This obviously wasn't the case, as the final polls turned out to be extremely accurate on Election Day. Then what was the problem? Why did we question the sample? Because people refuse to identify as Republicans. The polls weren't undersampling Republicans, Republicans were hidden as Independents. So when places like Gallup found huge support for Romney among Independents, they were actually mostly just Republican-leaners who preferred not to identify with the party.
So how do we get people to stop hating the GOP again? Well, we could start by not doing things like this, this, and this. The official RNC post-mortem report on the election and what went wrong was just released this morning. It's certainly not all what I would suggest, but it's a good start. Elections are by definition an organic thing. People have many reasons for supporting parties and candidates at every level (well, some just one), and thousands of things happen each election cycle to affect the outcome. The final result can't be controlled by the party or even the candidate at the top of the ticket, but we should definitely find those things that we can control and do better there.