The first families of the two major American political parties are proving to be a little bit of a thorn in their teams’ sides these days.

Former Florida governor Jeb Bush on Capitol Hill in Washington, D.C., on June 1. (J. Scott Applewhite — Associated Press)

Now, it’s become quite clear that Jeb Bush, son and brother to the 41st and 43rd presidents respectively, is on a quest to push his party away from the political extreme.

And, in fact, the efforts are somewhat comparable.

Both men, by virtue of their family’s standing in their respective parties, have a nearly un-matched political pulpit from which to express their views. And they’re using it more and more these days.

Both men also seem to see their party drifting away from what’s important. For Clinton, he wants a more close examination of the two sides’ visions for the future rather than a muddy bar fight, and for Bush, he wants his party to work with the other side more on issues like illegal immigration and the budget.

It also just so happens that both could be hurting their parties’ brands heading into the fall election.

Republicans have already used Clinton’s words — with great gusto — against President Obama. And we would expect the same on the GOP side, with Bush’s words being used against Romney and congressional Republicans.

Bush this weekend remarked that neither his father, George H.W. Bush, nor Ronald Reagan himself might have emerged from the 2012 Republican presidential primary. And last week, he said pretty much the same thing about his own presidential aspirations — that his views may not work in the Republican primaries of today.

He has also in recent days rejected Grover Norquist’s anti-tax pledge, and he said Republicans should accept a budget deal — which all GOP presidential candidates rejected at a debate last year — in which there would be $10 in spending cuts for every $1 in tax increases.

“I don’t believe you outsource your convictions and principles to people,” Bush said of the Norquist pledge during testimony before Congress earlier this month.

All of it, unfortunately for the Republican Party, paints the picture of a GOP that sells out to the conservative base and isn’t willing to compromise.

In other words, it’s the same picture that Democrats have been painting for a long time — to significant effect.

According to recent polling, the Republican Party’s favorable rating is hovering right around 40 percent, with more than half of Americans having a negative view of it. Republicans in Congress, meanwhile, have the approval of only around one quarter of Americans. Both ratings are worse than Democrats’.

The question from here, though, is whether it matters. And it may not.

The fact is that the GOP brand has been bad for a while. Even as the party scored huge gains in the 2010 election, it came largely despite the public’s unhappiness with Republicans in Congress and the GOP as a whole.

And in fact, the Republicans’ tendency to stand against whatever Democrats were proposing actually worked in the GOP’s favor, because what Democrats were doing was often unpopular and didn’t remedy the economy. By being steadfastly opposed to it, then, Republicans were able to make the case that they were the alternative.

Republicans think and hope the 2012 election, like 2010, will be all about Obama’s stewardship of the economy — and they may well be right.

“The Republican brand this fall will be defined by two things: Obama’s failures and Romney’s campaign,” said GOP strategist Dan Hazelwood. “Any messages unrelated to dealing with those points will be an admission of being out of touch, which is kryptonite to Obama.”

If the economy rebounds a bit, though, and/or the Obama campaign successfully turns it into a choice election (which is no easy task), then the GOP’s brand matters.

And Jeb Bush’s comments suddenly can be used against them.