Veterans, military construction and energy spending are funded through 2019, regardless of what happens with the rest of the federal budget.
Trump lashed out at Congress for failing to deliver the barrier, but many in the GOP say it is impractical, unrealistic and too costly.
The action comes with a government shutdown deadline less than two weeks away.
Congress will postpone a fight over money for President Trump’s border wall until after the midterm election, Appropriations Committee Chairman Rodney Frelinghuysen (R-NJ) announced Thursday.
Senate vote on three bills comes as time is running short before government funding runs out Sept. 30.
Some lawmakers fear that a pay freeze could be politically damaging in House districts with large numbers of federal employees.
Politicians from both parties are proposing ideas that would further drive up the deficit.
The top GOP leaders on Capitol Hill showed the president photos of the border wall and a complimentary newspaper story.
His stance contradicted what he said Tuesday and what his budget director told Republicans earlier in the day.
"I have no commitments or anything there," the U.S. Senate candidate says.