Updated

Democrats pushed the Senate toward approving more of President Obama's nominees on Tuesday as senators cleared the way for approval of the first of five nominees for the National Labor Relations Board and pivoted to other top diplomatic and law enforcement vacancies.

The Senate voted 64-34 to forbid delaying tactics against Kent Hirozawa's nomination to join the NLRB, an independent agency that helps resolve labor disputes. Democratic leaders were hoping for Senate approval by Wednesday of Hirozawa and Obama's two other Democratic picks for the board: Mark Gaston Pearce, the board's current chairman, and Nancy Schiffer, who like Hirozawa has been a long-time labor attorney.

Confirmation of at least one of them before Congress begins its summer recess this weekend would prevent the NLRB's work from grinding to a halt by late August. That is when Pearce's current five-year term expires, which would leave the agency with just two members -- short of the three legally needed for it to conduct business.

Senate movement on those and other nominations continued a trend started two weeks ago, when the two parties struck a deal that freed up seven stalled Obama nominations for votes. Though not all of the president's picks have clear paths -- his choice of Rep. Melvin Watt, D-N.C., for a housing regulator post seems in serious peril -- the detente has allowed Obama to get leaders in place at agencies including the FBI, the Labor Department, the Environmental Protection Agency and the Consumer Financial Protection Bureau.

In one turnabout, Democrats were expressing optimism that they would win the 60 votes needed to end Republican roadblocks against a vote on B. Todd Jones, whom Obama nominated in January to head the Bureau of Alcohol, Tobacco, Firearms and Explosives. The agency, which has not had a confirmed director since 2006, helps enforce federal gun laws.

Top National Rifle Association lobbyist Jim Baker said in an interview this week that the gun lobby would remain neutral on Jones, saying, "We find nothing in his background to concern law-abiding gun owners." The influential lobby has opposed past nominees and been a critic of the agency itself, arguing it has been too intrusive in its enforcement of gun laws.

"I think we're going to get it," Sen. Richard Durbin, D-Ill., the Senate Democratic vote counter, said Tuesday about efforts to round up 60 votes for Jones.

Many gun control groups have supported Jones' nomination, including Mayors Against Illegal Guns, led and largely financed by wealthy New York City Mayor Michael Bloomberg.

"Senators have come to understand that one of the reasons we have the worst gun violence problem in the world is the agency that's supposed to deal with it is rudderless and under-resourced," said Mark Glaze, the group's executive director.

Many Republicans still have qualms about Jones. Sen. Charles Grassley, R-Iowa, has complained that the nomination should not move forward because of two whistleblower complaints against him involving his work as U.S. attorney for Minnesota, a post he has held since 2009.

"It is imprudent and unwise for the Senate to give final consideration to any nominee where there is an open investigation into that nominee's conduct," Grassley said this week.

Jones has also been acting ATF director since 2011.

Also expected to win Senate approval this week is Samantha Power, a former Obama foreign policy adviser and long-time human rights activist, whom the president wants to become U.N. ambassador.

Power, who won a Pulitzer Prize for a book on how the U.S. responded to atrocities in Rwanda and Bosnia in the 1990s, has for years advocated intervention -- including military force -- to halt human rights atrocities. At her Senate confirmation hearing this month, she distanced herself from her 2002 call for a "mammoth protection force" to prevent Middle East violence, calling it a "remarkably incoherent answer."

Another of Obama's picks seemed to be listing as Senate Majority Leader Harry Reid said he would not schedule a pre-recess confirmation vote on Watt to head the Federal Housing Finance Agency. That agency regulates Fannie Mae and Freddie Mac, the taxpayer-backed mortgage giants who needed huge bailouts from Washington to survive the 2008 financial crisis and that many Republicans would like to replace or revamp.

The Senate was also expected to approve two Republicans to the NLRB by week's end: a pair of attorneys who have worked with employers on labor issues, Philip A. Miscimarra and Harry I. Johnson III.