A bill requiring a woman to get an ultrasound before having an abortion is poised to pass Virginia’s legislature this week, placing it on track to be signed into law by Gov. Bob McDonnell.

The bill, which could pass the Republican-led House of Delegates as early as Tuesday, is one of the stronger ultrasound laws passed by states in recent years. If it is adopted, Virginia will become the eighth state to require ultrasounds before abortions, a rule that anti-abortion forces hope will cause some women to change their minds but that women’s advocates call an effort to shame women and interfere with their privacy. The Senate, which is split evenly along party lines, narrowly adopted the bill this month.

Mr. McDonnell, a Republican who sponsored similar legislation when he was a lawmaker, initially voiced strong support. But the bill has drawn intense public attention, and a spokesman struck a more muted tone over the weekend, a shift that opponents said could mean that the governor might amend it before signing it. A throng of the bill’s opponents held a vigil outside the Statehouse on Monday in protest.

“If the bill passes, he will review it, in its final form, at that time,” said the spokesman, Martin Tucker. In Virginia, a governor can amend a bill after final passage by the legislature.

The nature and tone of legislation is particularly important for Mr. McDonnell, political analysts say, because he is seen as a possible contender for vice president on the Republican ticket and could be calculating how the bill will be perceived by a national audience.