"We're out of time. We need to act," Florida Sen. Bill Nelson said.
McConnell has been sidestepping questions about Donald Trump.
Democrats held the floor for more than 24 hours last week.
The bill is "the last chance we will have to address Zika for weeks," he said.
Julian Hattem 06/27/16 12:13 PM EDT
The GOP-led committee report has yet to be released.
Mark Kirk says the court upheld "access to health care for women."
The Senate will take up a House-passed Zika deal the White House has vowed to veto.
Cristina Marcos 06/26/16 06:00 AM EDT
Democrats have found their voice by reveling in being an especially disruptive minority.
McConnell said Trump has made "a number of very significant gaffes."
Sen. Ted Cruz called it a "wake-up call for internationalist bureaucrats."