Shelby said the president was "concerned" because the deal doesn't give him "everything he wanted."

ADVERTISEMENT "I told him I shared that, we all do. But realizing after I talked with him … that he's getting a good down payment," Shelby added, describing the president's tone on the deal.

The agreement struck on Monday night would fund roughly a quarter of the government through Sept. 30 and provide $1.375 billion for physical barriers along the border. Shelby added that the agreement would provide more than $22 billion on border security — a figure that appears to have resonated with the president.

"Will be getting almost $23 BILLION for Border Security. Regardless of Wall money, it is being built as we speak," Trump wrote in a tweet on Tuesday evening.

Trump's tweet signaled an openness to the agreement after telling reporters earlier in the day that he wasn't "thrilled" with the deal.

Shelby added that he was urging Trump to evaluate the bill in the context that it's "only a down payment." He maintained that questions about whether Trump will sign the bill are "premature."

"I've told him that, as I said a few minutes ago, that 'Mr. President, we had a good reception in the caucus today about this and we know it's multiyear, we know it's going to cost a lot of money but it's a good start,' " Shelby said.

Shelby's meeting with Trump comes after Senate GOP leaders, including Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.), were supportive of the agreement earlier Tuesday.

Sen. John Thune John Randolph ThuneSenate GOP sees early Supreme Court vote as political booster shot Romney backs pre-election Supreme Court vote, paving way for McConnell, Trump Senate GOP faces pivotal moment on pick for Supreme Court MORE (S.D.), the No. 2 Senate Republican, called the barrier money, which is significantly below the $5.7 billion Trump asked for during the previous 35-day shutdown, a "down payment" for the larger $25 billion Trump wants over several years.

McConnell also said he believes Trump should sign the agreement, saying the president "got a pretty good deal here."