House Republicans held a similar vote last month that was rejected by both sides of the aisle.
Rand's amendment is just one of the five to the legislation that could come up for a vote.
There is one offered by Sen. Jim DeMint (R-S.C.) that would repeal the Dodd-Frank Wall Street Reform passed by the Congress last year.
Another, from Sen. Olympia Snowe (R-Maine), would require federal agencies to more carefully assess the impact of proposed regulations on small businesses. However, Senate Majority Leader Harry Reid (D-Nev.) has implied that Snowe has yet to agree to limit debate time on her amendment.
"I should not act as the person who determines what amendments are offered and not offered, but when someone offers an amendment we should be able to work it to a conclusion," said Reid in reference to Snowe's language.
Reid also complained more generally that Snowe has yet to speak on her amendment. "Senator Snowe has offered amendment and has not said a single word about it," he said.
Sens. Ben Cardin (D-Md.) and Jeff Merkley (D-Ore.) also have two pending amendments related to mortgage payments and servicing.
Reid acknowledged in his morning remarks that while the underlying Economic Development Revitalization Act was important, it was not the "most important" legislation ever taken up by the upper chamber.
"Is this most important bill we have ever done?" asked Reid rhetorically. "The answer — of course is not, but it is an important piece of legislation."
The bill would increase funding for the Public Works and Economic Development Administration.