The proposal will include targeted sentencing reforms, according to an aide.
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 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.
Paul suggested Cruz lacks "personal relationships" with his Senate colleagues.
The six-month extension is headed to Obama's desk.
The Kentucky Republican said Congress is a "withering shadow."
The letter comes among Republican infighting over funding the organization.
"A dirty CR funding Planned Parenthood," Cruz says, would have ended the Speakership.