Shortly after the November election, I joked that maybe Republicans should all switch parties en masse just to confuse everybody. The media wouldn’t know whom to attack, other Democrats wouldn’t know whom to smear, and maybe the public would vote on ideas instead of party ID and other factors.

Unexpectedly, a new Hill poll backs up the soundness of the old switcheroo.

Respondents in The Hill Poll were asked to choose which of two approaches they would prefer on the budget, but the question’s phrasing included no cues as to which party advocated for which option.

Presented in that way, 55 percent of likely voters opted for a plan that would slash $5 trillion in government spending, provide for no additional tax revenue and balance the budget within 10 years — in essence, the path recommended by House Budget Committee Chairman Paul Ryan (R-Wis.) last week.

This was almost twice as many voters as opted for a proposal that would include $1 trillion in added tax revenue as well as $100 billion in infrastructure spending, and which would reduce the deficit without eradicating it.

Only 28 percent of voters preferred this option, which reflects the proposal put forth by Senate Budget Committee Chairwoman Patty Murray (D-Wash.) last week.

So, Paul Ryan for the win? Eh, not really. The same poll found that once voters were told which party supported which idea, the voters pulled the old switcheroo and backed the Democrats.

A plurality of voters, 35 percent, said they trust the Democrats more on budgetary issues, while 30 percent said they trust the Republicans more. A full 34 percent said they trust neither party.

The poll’s finding badly undercuts President Obama’s repeated claim that the American people are on his side in the budget standoffs. They’re not. They’re not on the side of his tax hikes or his increased spending. They’re not on the side of increasing the welfare state. You can still get a majority of Americans to recognize economic reality, which is welcome news.

But most voters are also not on the GOP’s side. As soon as they think they are on the GOP’s side, they run to the Democrats or declare themselves independent. That’s reflective of a party with a bad image problem that would have trouble selling anything.

The question is, what to do?

Much more on the next page.

CPAC this past weekend represented a changing of the guard. Three senators — Ted Cruz, Marco Rubio and Rand Paul — stepped up to become the next generation of GOP leaders. All three have cross-party appeal, and two of the three have cross-demographic appeal. The three are not all different versions of the same Republican. If one of these three ends up dominating, he will put an important stamp on the GOP. If it’s Paul, the GOP moves more into the isolationist, small-l libertarian direction. Rubio may nudge the GOP more in the direction of supporting a “comprehensive” immigration package, which would speed the path to citizenship for illegal aliens and, in my view, hasten the day that the GOP becomes a long-term minority party. Notice I didn’t say permanent. I don’t believe, as most Democrats and even many Republicans do, that demographic shifts already underway are going to create a permanent anything. If the next leader is Cruz, then we’re likely to see a GOP that remains a bit more security minded, and is a bit more aggressive in presenting core conservative ideas. But all of this will shake and shift as the three plus others, including Paul Ryan and Rick Santorum and other state leaders not yet fully in the national mix, make their moves.

Whoever the next leader or leaders turn out to be, there’s that GOP image problem lurking not even out of focus in the background. It’s not going to magically go away.