By Maeve Reston

CNN

COLORADO SPRINGS, Colorado (CNN) -- Sen. John Cornyn said Sunday he'd worked the phones all weekend trying to win support for the Senate health care bill and was "optimistic" the legislation would pass.

"It's hard," he told a small group of reporters when asked how negotiations were going between sessions at the Koch retreat. "But there's no excuse for failure. ... When people want to get to 'yes' you can have good faith negotiation and get them there."

"But it's going to be close," Cornyn said. He noted that he had been working directly with Republican Sens. Ted Cruz of Texas, Mike Lee of Utah, Ron Johnson of Wisconsin, Rand Paul of Kentucky and Dean Heller of Nevada to address their differing concerns about the bill.

When asked whether the Senate could wait until after the Fourth of July recess, he suggested that would weaken the bill's chances.

"We don't have the luxury of waiting around," he said. "It's not going to get any easier." The Texas senator described the period around August 1 as the "drop-deadline."

"We're trying to make sure we keep the rates down, stabilize the system, bring down rates, protect pre-existing condition coverage and do responsible Medicaid reform," Cornyn said.

Asked whether President Trump was doing enough to get the bill passed, he said: "We're trying to hold him back a little bit."

Cornyn, who serves as the Senate's whip, made the remarks to reporters while attending the Koch network's donor retreat here in Colorado Springs.

Ironically a number of his targets, who are either opposing the bill in its current form or remain uncommitted, were in the audience here. Sen. Ben Sasse, who is uncommitted, joked during a forum that he has a bruise just inside his left collarbone from Cornyn's thumb on his shoulder. As the Senate's number two Republican, it is Cornyn's job to pressure his colleagues to support the bill.

Cruz may offer two amendments this week that could ease the bill's passage, but he would not discuss his strategy during a brief conversation at the retreat. He said leaders were well aware of the policy priorities he has been pushing for the bill for many months.

On Saturday, US Rep. Mark Meadows --- who was intimately involved in the House healthcare negotiations --- said he could envision a scenario in which the Senate passed the bill this week, the House votes Friday and President Trump signs the bill on the Fourth of July.

"Wow, he is super optimistic," Cornyn responded when asked about that scenario. "That would be fine with me; I'm just trying to get through Thursday night --- the vote-a-rama," a reference to a series of votes on proposed amendments to the bill that could go late into the evening.