The Pentagon is reviewing locations in Colorado as potential alternatives.
Reid said New Hampshire and Iowa voters shouldn't be picking the next president.
The Arizona Republican called Putin's military intervention a "humiliating setback."
Ben Cardin said the proposal could be taken up as part of a larger criminal justice debate.
Western-state Republicans have voiced concerns about the legislation.
Julian Hattem 10/09/15 01:55 PM EDT
Democrats are proposing reforms to make it easier to bring refugees into the U.S.
Reid suggests nominations are being held hostage to "unrelated political fights."
The legislation does not specify how many refugees would be settled in the United States.
The legislation restricts federal funding for cities that don't comply with federal immigration law.
He said Republicans should bring a clean debt-ceiling bill to the floor "immediately."