"He could actually block this for a long period of time," Inhofe said, adding that lawmakers need to finish the bill by the end of next week.

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The NDAA's status as a must-pass piece of legislation makes it a lightning rod for hundreds of amendments, only a handful of which get votes. It also allows members to effectively block votes on any other amendments, or speeding up consideration of the bill, unless they also get guaranteed an amendment vote.

Paul said on Thursday that he isn't blocking the bill, but instead requiring leadership to run out the procedural clock.

Leadership had hoped to formally bring up the bill on Thursday, but that would require every senator to yield back the 30 hours of debate time required before the vote takes place. Instead, they'll vote to take up the bill on Monday evening.

"There's a normal process, you go through like 30 hours of this, 30 hours that, you have votes. It takes about four days to get a bill through. So no one can hold a bill or block a bill," Paul said.

But, he added, "I do believe that we should demand that there's an open debate with amendments."

Paul could block other senators from getting an amendment vote, unless they agree to give him a vote on his proposals.

The two amendments are similar to proposals that have emerged as sticking points during the defense bill debate in previous years. Paul hasn't said, yet, that he will block other amendments if he can't get a vote, but Inhofe signaled he thinks that's where the bill is going.

"We've been talking about this for three weeks. Remember what happened last year? Sure enough it seems to be happening again this year," Inhofe said, referring to the standoff over amendments.

Asked about giving Paul votes on his amendments, Inhofe added that it would encourage other senators to take the defense bill hostage.

"If you establish a policy that no matter what the amendment is, all you have to do is hold up everything and you do that, then you get 10 people doing that, and 20 people doing that," he said. "Then you never get a bill done."