Internet radio services are breathing a sigh of relief after the Senate approved a bill on Tuesday that would allow them to renegotiate a royalty rate that Web broadcasters say is too high. By law, Web sites like Pandora.com and Live365.com have to pay the performers and owners of the recordings they broadcast, and have been in a tug-of-war with record companies over the size of these payments. (Songwriters and music publishers are paid a royalty by radio stations and Web broadcasters; Web broadcasters also pay the performer.) Under the terms of the Webcaster Settlement Act, which was passed by the House on Saturday and now goes to President Bush for his signature, Web broadcasters have until Feb. 15 to negotiate with SoundExchange, the agency that collects and distributes the royalty. Under the current rate set by federal statute last year, said Tim Westergren, one of Pandora’s founders, his site has had to pay 70 percent of its gross revenue for this performance royalty, and will have to shut down if it is not reduced.