Hochberg needs to be confirmed before July 20 or run the risk of leaving the bank without a quorum to act on many of the transactions before it.
The bank's process requires at least three of five board of directors to approve transactions.
Besides Hochberg, the terms of two other board members are set to expire in July and the Obama administration has not yet nominated anyone for those slots.
The conservative Club for Growth has asked Senate Republicans to oppose the nomination until another plan is implemented for reducing the "bank's authority with the ultimate goal of ending its charter completely."
Hochberg's nomination has gotten nods from groups such as the National Association of Manufacturers (NAM) and the U.S. Chamber of Commerce, which argue that the bank helps U.S. businesses remain globally competitive.
He was easily confirmed in 2009 — by unanimous consent in the Senate — and saw the bank through a tough reauthorization fight last year that allowed the Ex-Im to increase the total financing the bank can guarantee — to $140 billion from $100 billion and renew its charter for three years, through 2014.
The House and the Senate provided broad support for the reauthorization bill.
The bank, created in 1934, provides loan guarantees to foreign companies that want to do business with U.S. exporters.
Last year, the bank provided more than $35.7 billion in financing and increased small-business financing more than 70 percent to $3.3 billion between 2008 and 2012, according to the bank.
This story was updated to reflect a revised vote count.