Senator Hoeven says the Senate is about four votes short of enough to override a veto by President Obama on a measure that would authorize the Keystone XL pipeline.
Obama has said he objects to the Keystone legislation because it takes the decision out of the hands of the executive branch.
The chamber's 54 Republicans are all expected to support the bill, as well as nine Democrats. But that's not enough to achieve the two-thirds majority that's necessary to override a veto.
Last week the House approved the legislation green-lighting construction of the 1,179-mile pipeline.