LAS VEGAS (AP) _ The stifling desert heat radiates from the sidewalk outside the Tropicana Hotel where the band that for years provided the music now walks a picket line to protest its replacement: taped music.

Inside the lavish resort, singers lip-sync and dancers kick their legs to recorded music during the popular Folies Bergere show's twice-nightly performances.

Musicians are locked in a fight for survival at the Tropicana and two other Strip resorts, where cost-conscious managers also want to replace live music in production shows.

''The musicians ultimately make the product that puts musicians out of work,'' lamented Mark Tully Massagli, leader of Musicians Union Local 369. ''Think of the irony of that.''

The conversion to tape now affects about 45 full-time musicians, but it has raised passions among many more who feel spontaneous entertainment is being sold out by gaming corporations.

''We can't have this town - which was built on live entertainment - go the other way,'' said singer Sammy Davis Jr. ''Don't let them do this to us.''

Davis and a few other big name entertainers gathered recently to back the musicians.

''If we lose live music in this town, we've got serious problems,'' said comedian Jerry Lewis.

Lewis and Davis were appearing together at Bally's, which plans to replace the 19 musicians backing its Jubilee production show with taped music but keep live musicians in its main showroom.

Hotel officials say musicians are an expensive luxury not found in Atlantic City, N.J., hotels, which allow taped music and synthesizers in place of live performances.

''We're not doing away with musicians in the Celebrity Room,'' said Robert Ostrovsky, a Bally's executive. But ''we feel taped music is appropriate for production-type showrooms.''

The 14 union musicians who backed the Folies Bergere show at the Tropicana walked off their jobs June 3, upset over the hotel's unwillingness to budge on the issue. The show was closed while a tape was prepared, and reopened June 25 to what hotel officials say are increasingly full audiences.

''We're doing very well with it,'' said hotel spokesman Ira David Sternberg.

Musicians at Bally's and the Flamingo Hilton, meanwhile, have stayed on the job despite the refusal of the hotels to increase their offer of two to four musicians at each hotel on the payroll and severance pay to the others.

Officials at the three resorts sent letters to the musicians last week informing them they would not be needed further when they implement their final offer on July 26 and go to taped music.

Perhaps more ominous, however, to the estimated 250 musicians who make a living in the hotels is a plan by the resorts to pay musicians only for the shows they actually perform.

Many entertainers bring their own bands to Las Vegas, limiting work for the Las Vegas musicians.

Under the contract that expired June 1, musicians were guaranteed their $654.71 a week salary for at least 38 weeks a year.

The pickets have tried to rally support by warning that musicians who fill the city's symphony and small jazz bands may be forced to leave town to find work, leaving a cultural void in the city.

They also took out a $12,000 ad in the Los Angeles Times warning tourists of the strike.

And the union has won a few victories in negotiations. Massagli said the Stardust Hotel has agreed to a contract keeping musicians at its long-running Lido de Paris show and the Union Plaza has agreed to live music at its smaller production show.

But the major Strip resorts usually set the trend, and that is where the musicians believe may be their last stand.

''Our entire future is at stake here,'' Massagli said. ''This is for our very survival.''