(New throughout, adds details on stimulus package, other airlines)

CHICAGO/WASHINGTON, July 30 (Reuters) - United Airlines told its pilots it may need more furloughs than originally planned this year and next due to a worsening industry outlook as COVID-19 cases rise, unless there is another bailout or unions agree to reduce costs, a memo reviewed by Reuters showed.

The internal memo, which United confirmed was sent to pilots on Thursday, comes as unions lobby U.S. lawmakers to extend a $32-billion aviation stimulus plan that protected aviation workers' pay and jobs through September.

A second bailout, coined CARES Act 2.0, has Congressional support but could face hurdles among some Republican senators, people familiar with the matter said.

Airlines are suffering their worst crisis in history due to COVID-19, which crushed the U.S. economy in the second quarter.

Chicago-based United does not forecast a recovery until a vaccine is mass produced, something it does not expect until late 2021.

But once a recovery arrives, airlines say they need trained workers on hand to operate an industry that is vital to the global economy.

Tens of thousands of airline jobs are at risk.

FURLOUGH WARNINGS

"There are really only two ways to mitigate the full impact of furloughs. The first is another stimulus bill," United's head of flight operations, Bryan Quigley, said in the memo.

The Chicago-based airline had previously said it would furlough 2,250 pilots between Oct. 1 and the end of 2020 and another 1,650 in 2021, depending on demand.

United did not provide additional comment.

It has already told 36,000 union workers, about 45% of the total, that their jobs are in jeopardy.

The message follows a warning from budget carrier Spirit Airlines this week that 20-30% of workers may be furloughed in October.

Others including low-cost Allegiant and Hawaiian Airlines also warned this week of furlough notices, while United and American Airlines extended deadlines for some employees to accept voluntary furloughs or early retirements.

Aside from federal aid, some of which must be re-paid, U.S. airlines have tapped new debt to boost liquidity during the crisis.

United's memo warned that those loans will hinder its ability to buy new planes, hire new pilots, or bring back pilots who were furloughed.

Delta Air Lines and Southwest Airlines, which enjoy a stronger debt position than American and United, have said they can minimize or avoid involuntary furloughs thanks to strong take-up for employee buyouts. (Reporting by Tracy Rucinski and David Shepardson Editing by Chris Reese, Nick Zieminski and David Gregorio)