With U.S. Rep. Ron Paul of Texas remaining as the lone major challenger, Romney has become the presumptive party presidential nominee, needing fewer than 200 delegates to reach the required 1,144 votes necessary to seal the deal. Paul, however, is working the state party caucuses to try to accumulate delegates as well heading into the convention, but has fewer than 100.
As of Thursday, CBSNews.com indicated Romney had 934 delegates and Paul had 92.
Up on Tuesday's dance card: Nebraska, with 35 delegates, and Oregon, with 28 delegates.
Voters in Nebraska Tuesday pick their candidates to succeed retiring U.S. Sen. Bob Nelson.
In the Republican race, two big names endorsed two different candidates.
Sarah Palin, the 2008 vice presidential candidate, backed underdog state Sen. Deb Fischer.
In a letter, Palin said, "We admire your conservative principles and know that you will not go to Washington to amass great wealth or power," the Omaha World-Herald reported. "You will go to Washington to serve the people of Nebraska, protect our Constitution and work for common sense solutions to help restore America. We are happy to support you and have asked SarahPAC to send a financial contribution to your campaign."
Fischer faces state Treasurer Don Stenberg and state Attorney General Jon Bruning, who picked up the endorsement of former U.S. Sen. Rick Santorum, who last month ended his bid to be the party's standard-bearer in November.
"Jon Bruning is a trusted conservative who is unapologetically pro-life, will fight to reduce the size of the federal government and will ensure that the government spends less and does not tax more," Santorum said in a statement.
The winner could face former Gov. Bob Kerrey, who will be trying to keep Nelson's seat in the Democratic fold. Kerrey, who also once represented Nebraska in the U.S. Senate, faces four challengers on the Democratic ballot.
Bruning began as the front-runner in the GOP tilt, and even his chief rivals acknowledge he still leads the pack, the World-Herald said.
Bruning also has proven to be an adept fundraiser, swamping his opponents, the World-Herald said. As of the end of March, Bruning had raised $3.3 million, compared with $628,000 for Stenberg and $356,000 for Fischer.
While Bruning has outraised his rivals, some observers note the field has been leveled by the infusion of cash from outside political committees backing Stenberg.
The Senate Conservatives Fund, created by Tea Party leader U.S. Sen. Jim DeMint of South Carolina, has pumped at least $1.3 million into the race, mainly in television advertisements touting Stenberg as a "genuine conservative."
Also, the anti-tax Club for Growth spent $720,000 in the race, also primarily on television ads critical of Bruning's conservative bones.
Kerrey, too, also has benefited from donations from people or groups outside of Nebraska, The New York Times reported. Kerrey collected $30,000 in recent days, including a $1,000 donation from Barbra Streisand and $5,000 from S. Parker Gilbert, the former chairman of Morgan Stanley.
Fischer's camp says she's still in it, pointing to a campaign-commissioned poll in April that indicated Bruning led with 30 percent support, Stenberg had 21 percent and Fischer was at 19 percent, but improving. More important, the Fischer poll indicated 28 percent of likely Republican voters were undecided.
"Momentum is on our side," Fischer campaign manager Aaron Trost told the Omaha newspaper.
Even though Fischer's poll indicated the race may have tightened, it still gives Bruning a huge edge, said Tim Hill, a political scientist at Doane College in Crete, Neb.
"It's not insurmountable ...," Hill said, cautioning, "For Bruning to lose a lead like that, he'd have to really [do something] to lose it."
Nebraskans also will vote on a constitutional amendment that would change the term limits for state lawmakers from two terms to three, KETV, Omaha, said.
Voters approved a two-term limit in 2000.
The 5th Congressional District in Oregon is perhaps the state's most competitive, but observers say they would be shocked if incumbent Kurt Schrader, a Democrat, didn't win in November.
They look to Schrader's 5-percentage point victory during what President Obama called a "shellacking" in 2010 by Republicans and no GOP opponent has recently reported any substantial money, Roll Call reported.
Plus, the contest so far has avoided national attention.
In the statewide attorney general's race, Democrat Ellen Rosenblum is ahead of primary rival Dwight Holton -- or former federal prosecutor Holton leads retired Appellate Judge Rosenblum, depending on the poll, The (Portland) Oregonian reported.
However, no matter who was leading in the run-up to Tuesday's primary, the polls seem to agree at least 50 percent of likely primary voters remain undecided.
Rosenblum's poll, conducted in early May, showed her taking a 32 percent to 17 percent lead over Holton.
Holton's pollster, however, showed him ahead of Rosenblum 27 percent to 23 percent.
No one filed in the Republican primary for the office. The Oregonian said the winner of the Democratic primary could take office as soon as July 11, the day outgoing Attorney General John Kroger takes over as president of Reed College.