When Virginia Gov. Robert F. McDonnell (R) asked antiabortion zealots in the General Assembly last week to soften the controversial ultrasound bill, he faced a dilemma in explaining his move: Shall I appear ill-informed or weak-willed?

McDonnell chose the former. He says he just didn’t realize the measure he had been broadly supporting would require many women desiring to end a pregnancy to undergo a particularly invasive ultrasound in which a probe is inserted in the vagina.

Because of McDonnell’s intervention, the bill soon headed for his signature would require only an abdominal ultrasound, performed outside the belly. That’s still an outrageous violation of women’s rights, for abortion defenders (like me). But abortion opponents view it as a disappointing compromise.

I’m skeptical that the governor’s explanation is the whole story. I agree with the hard-core social conservatives who said he had “suddenly gone squishy,” as one blogger wrote, when faced with an outpouring of opposition. That included having the law (and by extension, the state) become a punch line for late-night comedians.

Still, I credit McDonnell with being true to the political profile he presented to Virginia voters when he won a landslide victory in 2009. He’s consistently called himself a “pro-life” Republican but one who didn’t want to emphasize social issues.

By acting to temper the bill, while still promising to sign it, McDonnell honored both halves of that promise. He also signaled his dislike of an even more far-reaching antiabortion proposal, to confer “personhood” rights on a fetus. The bill died in the Virginia Senate.

Unfortunately for McDonnell, the nuances of his position drowned quickly in the raging ideological whirlpool that is abortion politics, particularly at the national level.

It doesn’t matter to the Democratic Party — much less MSNBC commentators or “Saturday Night Live” satirists — that McDonnell repeatedly urged GOP legislators not to “overreach” on social issues. They don’t care that he’s been emphasizing, every chance he gets, that his priorities are economic development and other “kitchen table” topics.

From the left’s perspective, what matters is that McDonnell is preparing to sign the second bill in a year designed to restrict and regulate abortions. The earlier one raised building standards for clinics that perform abortions.

As a result of the uproar, he has probably sacrificed whatever chance he had of being picked as the GOP vice presidential nominee this year, said a wide range of political analysts, including Republicans sympathetic to the governor.

Assuming that the Republican presidential candidate is Mitt Romney, it would be much harder for him now to tap McDonnell as a running mate. The two of them would immediately have to devote time to defending the ultrasound bill, in addition to McDonnell’s controversial 1989 master’s thesis saying, among other things, that working mothers hurt families.

“I think the moment in the sun is over,” said a Republican source, who spoke on condition of anonymity to speak candidly about the governor’s prospects.

The ultrasound controversy “was probably very unhelpful to the calculus that Romney will make at the convention. Together with the thesis, this creates a second object of ridicule,” the source said.

The other big risk to McDonnell is that hard-core conservatives in the General Assembly are hijacking his three-year effort to rebrand the Virginia Republican Party as one devoted to “results-oriented conservatism” rather than polarizing social issues.

McDonnell didn’t help his own cause when he signed a bill to repeal a longtime law limiting firearms buyers to one handgun a month— which he supported when it originally passed.

“McDonnell has done what he could to try to tamp down the social issues. But still, the number of bills on so many fronts is so high, I think it’s going to be a tough sell for him to say, ‘I moderated the crazy,’ ” Del. Robert H. Brink (D-Arlington) said.

Republicans aren’t the only ones in Richmond who risk overreaching. The Senate Democrats’ move Wednesday to block approval of the budget could alienate the public, too.

But the GOP is dominant now, and it’s pushing harder than before on issues that its own leader wants to de-emphasize.

If Democrats win Virginia in November as a result, with both the White House and U.S. Senate in play, the Republicans might wish they had better heeded McDonnell’s counsel.

I discuss local issues at 8:51 a.m. Friday on WAMU (88.5 FM). For my previous columns, go to postlocal.