Winning senators' support for the broad contours of a bipartisan agreement underway to combat gun violence looks like easy, but keeping their support intact for the eventual legislation will be much harder, reported CNBC on Monday.

Senators are now racing to finish writing the bill already signed by 10 Republican members this week in hopes of passing it next week before a scheduled July 4 recess, and they're running into complicated challenges, according to the report.

"The high-wire act facing them requires writing a bill that can satisfy Democrats' demand to take meaningful strides without alienating Republicans, who are deeply sensitive to fears that any sort of action could cause a weakening of gun rights," said the report.

The goal of GOP leaders is to get about half their 50-member caucus on board with the bill, said CNBC.

The biggest hurdles so far are "red flag" provisions -- specifically, assuring due process before gun rights are stripped from dangerous individuals -- and background checks for Americans aged 18 to 21, it added.