Sen. John Cornyn, R-Texas, told Politico this week that he’s confident in the Senate's bipartisan gun safety bill despite potential criticism from conservatives.

Last weekend, Cornyn was booed by attendees of the Texas GOP convention during his address. Cornyn has been working closely with Democrats in recent weeks, after a mass shooting at an elementary school in his home state, on legislation to curb gun violence.

"I'm committed to getting a result here. And I understand that some people [in Texas] are unwilling to listen," Cornyn told Politico on Monday. "I was there to explain my position and why I believed it would not jeopardize Second Amendment rights of law-abiding citizens. And some people didn’t want to hear about it."

When asked if this could affect his standing, Cornyn said, "Well, I guess we'll find out. I don’t think so."

Sen. John Kennedy, R-La., who opposed the legislation, said that Cornyn "exercises power materially and intelligently. And he's been around the block a few times. He knows who he is, and he knows what he believes."

Kennedy also said that Cornyn's work on the bill has "helped" his standing in the GOP conference, but Politico reports that some Republican senators have said that Cornyn could lose some stock among his colleagues, as many oppose the legislation.

Rep. Kevin Brady, R-Texas, noted that in the state, "booing top elected officials is somewhat of a tradition," and said that this "tends to happen pretty regularly" to Cornyn, who has come under criticism from the right before.

"The conservative base isn't John Cornyn's constituency, per se," said Rep. Pat Fallon, R-Texas. When asked how Cornyn's work is received by his fellow Texas representatives, Fallon said: "You know how it is with the other chamber, with the powdered wigs and the British accents over in the Senate. Typically what they're doing doesn’t come up."

• Cornyn: Sticking Points on Gun Safety Bill, Which Might Get Pared Down
• GOP Sen. Cornyn: Democrats Have Nearly 'Run Out of Rope' in Gun Reform Talks