NEWARK, N.J. (CBSNewYork/AP) — The judge overseeing U.S. Sen. Bob Menendez‘s corruption trial said he won’t dismiss any charges against the New Jersey Democrat.

Judge William Walls rejected defense lawyers’ arguments that the allegations against Menendez didn’t meet the new, narrower definition of bribery under a 2016 Supreme Court ruling that reversed the conviction of Republican former Gov. Bob McDonnell of Virginia.

In recent months, that same ruling has led to the overturning of convictions of three former public officials, including former New York Assembly Speaker Sheldon Silver and former New York Senate Majority Leader Dean Skelos.

Menendez arrived at the federal courthouse in Newark on Monday with his daughter by his side, and shook hands and thanked supporters.

The decision was a major defeat for Menendez and a huge victory for prosecutors, who warned that dismissing the charges would torpedo nearly all other bribery cases and open the door wide to graft.

Prosecutors rested their case last week following six weeks of testimony. The defense will now begin presenting its case.

Menendez is charged with accepting free flights on a private jet and other gifts from wealthy Florida doctor Salomon Melgen in exchange for pressuring government officials to take actions favorable to the friend’s business interests.

The indictment charges Menendez accepted the flights on Melgen’s private plane and other gifts over a seven-year period in exchange for pressuring executive branch officials on behalf of Melgen in an $8.9 million Medicare billing dispute and a contested contract for port screening equipment in the Dominican Republic.

It also charges that Menendez helped get visas for Melgen’s foreign girlfriends.

The two men deny the charges and say the gifts were a result of their longtime friendship.

The most serious charge Menendez and Melgen face, honest services fraud, is punishable by up to 20 years in prison.

Last week, the judge surprised some when he set aside what was expected to be the trial’s central issue: whether Menendez’s meetings and other dealings with government officials could be considered “official acts” under the McDonnell ruling’s new definition.

Instead, the judge focused on the “stream of benefits” theory, which in the past held that a bribe doesn’t have to be made with the intent to prompt a specific official action.

Menendez’s and Melgen’s attorneys argued that language in the McDonnell decision requires that an alleged bribe must be given in exchange for an official taking an action — or agreeing to take action — on a specific “question, cause, suit, proceeding or controversy.”

Menendez attorney Abbe Lowell argued the prosecution used a “mix-and-match” strategy to pair up Melgen’s gifts with actions Menendez took over the years, without establishing direct connections.

“They are one, two years apart,” he said. “Sometimes the bribe is allegedly for something three months before.”

In response, Justice Department attorney Peter Koski argued that the Medicare dispute and the port contract were the specific matters at issue and that a public official doesn’t have to specify how he will perform his end of the bargain.

In a brief filed Saturday, prosecutors cited cases since the McDonnell ruling in which, they said, federal appeals courts have left the stream of benefits theory undisturbed. Invalidating it, they wrote, would “jettison the vast majority of bribery prosecutions, and broadly legalize pay-to-play politics.”

(© Copyright 2017 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)