Organized labor is deeply worried about what happens after Tuesday.

By many measures, labor unions have been the Republicans’ fiercest, biggest-spending opponents in this year’s campaign, laying out more than $200 million in hopes of safeguarding the Democratic majorities in the House and Senate.

So it should be no surprise that Republicans, who appear to stand a good chance of winning control of the House, are signaling that they plan to push bills and strategies to undermine labor’s political clout and its ability to grow.

“Republicans are likely to pursue a version of what Samuel Gompers often said: ‘Reward your friends and punish your enemies,’ ” said Joseph McCartin, a labor historian at Georgetown.

One bill that is popular among Republicans would prohibit employers from ever agreeing to unionization through “card check,” a process often used today in which an employer recognizes a union as soon as a majority of workers sign pro-union cards  without holding a secret-ballot election. Another bill would severely crimp labor’s campaign spending by barring unions from using any portion of a union member’s dues for political purposes unless the member first gives written permission.