If not, "Marcellus Shale cannot be resolved this year," according to the letter, with some of the strongest wording yet, signed by Senate President Joe Scarnati (R., Jefferson); Senate Majority Leader Dominic Pileggi (R., Delaware); and Senate Appropriations Chairman Jake Corman (R., Centre).
Democrats who control the House reiterated that they would return to Harrisburg only if a deal had been brokered - a possibility that dims with each passing day. There were no talks Wednesday, and none yet scheduled for Thursday.
"The Senate Republicans have failed at every turn to act responsibly on this issue," said Brett Marcy, spokesman for House Majority Leader Todd Eachus (D., Luzerne).
Marcy said the House had already passed two shale tax bills with bipartisan support, and could not negotiate on a third piece of legislation without Senate cooperation.
"They continue to make excuses and punt the issue back to the House," Marcy said.
House Republican leaders said they would send Rendell their proposal for a shale tax Thursday.
In their letter to Rendell, the three Senate Republican leaders reiterated their caucus' position that they would support a 1.5 percent tax on the market value of gas from wells producing more than 150,000 cubic feet of gas. That rate would apply for the first five years of production, at which point the tax would increase to 5 percent.
Rendell has said he cannot sign such a proposal into law.
And late Wednesday, Rendell spokesman Gary Tuma said there was very little in the Senate GOP letter indicating that Republicans were willing to negotiate.
Said Rendell in a statement: "I am extremely disappointed in the Senate and House Republicans for failing to provide any reasonable compromise on a severance tax rate. Not only have they broken their promise to the people of the commonwealth, they have left the local governments in serious financial trouble and have robbed the state of resources necessary to protect our environment."
Rendell originally proposed a 5 percent tax on sales of the extracted gas, and an additional 4.7 cents for every 1,000 cubic feet produced.
During recent negotiations, however, he offered to phase in a levy on gas extracted from the rich shale formation, which lies beneath most of the state, starting at 3 percent next year and topping out at 5 percent.
The bill the House approved last month calls for a much heftier rate: a levy of a minimum of 39 cents per 1,000 cubic feet (or about 10 percent) of natural gas produced.
Contact staff writer Angela Couloumbis at 717-787-5934 or acouloumbis@phillynews.com.