The Congressional Budget Office on Thursday narrowed its projections for when Treasury might run short on money if lawmakers don't raise or suspend the country's debt ceiling.

The CBO now estimates that Treasury might risk defaulting on some payments in the first half of October.

Previously, it had predicted that the so-called X date -- the point when Treasury won't have enough cash and revenue on hand to pay all bills in full and on time -- would come sometime in the fall.

"The range of possible dates has narrowed as the budget outlook for this year has become clearer and CBO has increased its estimate of the Treasury's net borrowing needs," the agency noted in a new report.

Related: Mnuchin cites September as possible debt ceiling crunch

Currently the legal borrowing limit is set at $19.81 trillion. Since mid-March, when the most recent debt ceiling suspension ended, Treasury has been using special accounting measures to allow the government to continue borrowing as needed.

But those measures, by the CBO's estimate, will be tapped out between early and mid-October.

The CBO cautioned that the estimate is just its best gauge as to when Treasury is most likely to run short. But, it noted, "the timing and magnitude of revenues and outlays over the next few months could vary noticeably from CBO's projections."

The final word on when the debt ceiling must be raised will come from Treasury Secretary Steven Mnuchin. Earlier this month, he told a House Appropriations subcommittee, "I am comfortable saying we can fund the government through the beginning of September. I would prefer not to give a range at this time."

And on Thursday at a White House press briefing, Mnuchin dodged some specific questions on the issue, instead reiterating what he's said on numerous occasions.

"I think that Congress should act quickly, raise the debt ceiling and we should pay our debts on time."

In particular, Mnuchin has urged lawmakers to take action before they leave for their August recess.