FAIRFAX, Va. — Republican Mitt Romney accused President Obama on Thursday of ‘‘failing American workers’’ by ignoring Chinese trade violations, and seized on new Federal Reserve attempts to boost the economy as proof the administration’s policies are not working.

Obama campaigned as commander in chief after the violent deaths of four US officials at a diplomatic post in Libya. ‘‘No act of terror will go unpunished . . . no act of violence shakes the resolve of the United States of America,’’ he said.

CAROLYN KASTER/ASSOCIATED PRESS

President Obama appeared in Colorado on Thursday.

The president spoke in Colorado and Romney in Virginia with less than eight weeks remaining in a close campaign for the White House. The two states are among a handful likely to settle the race, and most polls rate Obama a shaky favorite.

With campaign costs mounting, Romney and Obama competed for the most innovative fund-raising appeal.

The Republican challenger’s campaign urged people in an e-mail to make a $15 donation for a chance to join ‘‘Mitt on board the campaign plane for an exciting day on the campaign trail — at 30,000 feet!’’

Singer Beyonce Knowles and hip-hop-artist-husband Jay Z countered. ‘‘Jay and I will be meeting up with President Obama for an evening in NYC sometime soon,’’ she wrote. ‘‘And we want you to be there.’’ As with a day aboard Romney’s chartered jet, a donation was requested for a chance to win.

Only the fine print of both fund-raising appeals made clear that no contribution was necessary to win.

Romney’s focus on the economy followed a one-day campaign detour into a foreign-policy thicket that left him bruised and his quarry largely unscathed. He made little mention during the day of the events in Egypt and Libya that he had cited Tuesday as evidence of national security weakness on Obama’s part.

The issue intruded, though, when a heckler at Romney’s rally yelled out, ‘‘Why are you politicizing Libya?’’

The crowd responded with chants of ­‘‘U-S-A’’ and supporters tried to place a Romney/Ryan placard in front of the heckler’s face.

‘‘We’re going to crack down on China,’’ the former Massachusetts governor vowed in an appearance in the Virginia suburbs around Washington, D.C. He spoke after his campaign unveiled a television commercial claiming that China has outpaced the United States in new manufacturing jobs since the president took office. ‘‘Seven times Obama could have stopped China’s cheating. Seven times he refused,’’ it says.

White House spokesman Jay Carney told reporters that all the actions the administration has initiated at the World Trade Organization to rein in China have been successful. Obama’s campaign said he has brought as many cases challenging China trade policies in 3½ years as former President George W. Bush did in eight.

Pa. court considers legality, timing of new voter ID law

PHILADELPHIA — Pennsylvania’s state Supreme Court justices aggressively questioned on Thursday whether a politically charged law that requires photo identification from all voters should take effect for the Nov. 6 presidential election and whether it guarantees the right to vote.

With the election just 54 days away, the justices did not say when they will decide, although lawyers in the case expect them to rule before the end of September.

The high court appeal follows a lower court’s refusal last month to halt the law from taking effect. The six-month-old law — championed by Republicans over the objections of Democrats — is now part of the heated election-year political rhetoric in a state whose 20 electoral votes make it a major player in electing a president.

The rules — now among the nation’s toughest — were already a lightning rod for supporters of President Obama, a Democrat, when a top state Republican lawmaker said in June that the ID requirement ‘‘is going to allow’’ the GOP’s presidential nominee, Mitt Romney, to win the state of Pennsylvania. The law has inspired protests, warnings of Election Day chaos, and voter education drives.

The six justices — three Republicans and three Democrats — saved their most aggressive questions for lawyers representing the state and Governor Tom Corbett, a Republican who signed the law in March. A couple of exchanges became testy during 80 minutes of arguments.

Justice Thomas Saylor, a Republican, questioned the state’s lawyers about whether the law actually requires the state to ensure that every registered voter be able to vote, even those who cannot get a valid ID. Justice Debra Todd, a Democrat, flatly suggested the law is unconstitutional.

Justice Seamus McCaffrey, also a Democrat, pushed the state’s lawyers to explain the Republican rationale used to pass the law and whether the Legislature deserves deference for its decision to pass a politically divisive law that ‘‘is now going to trample the rights of our citizens.’’

Republicans have long suspected ballot-box stuffing in the Democratic bastion of Philadelphia, and they contend the photo ID requirement will solidify public confidence in elections. But Democrats say it is a ruse to suppress the votes of minorities, the poor, the young, and others considered more likely to vote for Obama.

In the opening statement by a lawyer for the plaintiffs, justices asked whether it would be acceptable for the photo identification requirement to be phased in over a longer period of time — say, a period covering two federal elections.

The lawyer, David Gersch, replied that it would, as long as the law guarantees the right to vote to each registered voter, even someone who cannot get a photo ID that is among several types that are valid under the law. Other states, such as Georgia and Michigan, have made such guarantees in their laws, Gersch said.

But under Pennsylvania’s law, ‘‘there’s too little time, there’s too many people affected, and there’s no place in the statute that guarantees that qualified electors can get the ID they need to vote,’’ Gersch told the justices.

Lawyers for the state argued that the justices should defer to the Legislature’s decision on a policy matter and to the lower court judge’s decision not to halt the law.

Ryan votes for spending bill $19b higher than his own plan

WASHINGTON — Republican vice presidential candidate Paul Ryan on Thursday went along with a stopgap spending bill in the House that avoids a government shutdown but carries a price tag $19 billion higher than the budget he wrote in his role as a congressman.

Ryan, the top budget writer in the House, voted for a temporary spending bill that lets Congress keep government open for another six months. That allows lawmakers and President Obama to put off dicey budget talks until after the Nov. 6 election.

Politics, though, were not far from Ryan’s first day back to Congress since joining Mitt Romney’s presidential bid. He met informally behind closed doors with Republican lawmakers in what aides described as a meet-and-greet event.

The House chamber later erupted in a loud cheer — mostly from the Republican side — when Ryan entered the hall. Ryan held court in the rear of the chamber as back-slapping colleagues surrounded him. Among those congratulating him was the top Democrat on the House Budget Committee, Representative Chris Van Hollen of Maryland, with whom Ryan has an adversarial but friendly relationship.

Ryan did not deliver remarks on the House floor ahead of the vote approving spending far greater than his budget outline.

‘‘The fact that a stopgap measure is necessary is another indictment of the president’s failure to lead,’’ said Ryan’s campaign spokesman, Brendan Buck.

Democrats worked to highlight components of Ryan’s budget plan that would fundamentally change seniors’ health care and young voters’ education options.

GOP’s McConnell hires strategist from Tea Party

FRANKFORT, Ky. — Senate Republican leader Mitch ­McConnell has hired some Tea Party credibility.

The Kentucky Republican has hired Jesse Benton, who steered the presidential campaign of Texas congressman Ron Paul, to head his reelection campaign in 2014. McConnell says he is committed to running a presidential-level campaign, and hiring Benton shows heknows he needs to win support from conservatives. The hire, along with McConnell’s $6 million campaign war chest, could also scare off potential Tea Party challengers.

In 2010, McConnell backed Trey Grayson for Senate, but Paul’s son, Rand, won instead — with Tea Party support. Now, Rand Paul says he supports ­McConnell’s decision to hire Benton.