Violence declined in Iraq, then Shiite-on-Shiite fighting erupted in Basra. Army Gen. David Petraeus, the top U.S. commander in Iraq, last week recommended a plan to suspend troop withdrawals in July.

As the level of violence dropped, war-related arguments favored presumptive Republican nominee Sen. John McCain of Arizona, an outspoken supporter, The Wall Street Journal reported Wednesday. As violence began an uptick, Democratic presidential contenders Sens. Barack Obama of Illinois and Hillary Clinton of New York have begun reiterating their positions that the United States needs to withdraw from Iraq.

The question of whether voters think it's more important to leave or succeed in Iraq is "a very hard question to answer," said Andrew Kohut, Pew Research Center president.

Pew surveys indicate a near-even split on whether troops should stay in Iraq until it is stable or return home, he said.

"The public certainly doesn't want troops there indefinitely, but a desire to succeed is implicit in their views about Iraq, too," Kohut said. "Bottom line, I say the public overall is divided between the two."