Republicans objected to the inclusion of money for Planned Parenthood.
Sen. Chuck Grassley is currently blocking 22 State Department nominees.
The request comes as Russia is stepping up its military activity in Syria.
The proposal will include targeted sentencing reforms, according to an aide.
The House voted to advance a spending bill to avoid a government shutdown.
The move could undercut President Obama's nuclear deal with Iran.
McCain said Putin has stepped "into the wreckage of this administration's Middle East policy."
The leadership votes will happen a week from Thursday.
The Senate will take a procedural vote on taking up the bill this week.
The House is expected to approve the bill later in the day.